diff --git a/changelogs/fragments/1199-docker_image-push.yml b/changelogs/fragments/1199-docker_image-push.yml
new file mode 100644
index 00000000..f861ea7e
--- /dev/null
+++ b/changelogs/fragments/1199-docker_image-push.yml
@@ -0,0 +1,5 @@
+bugfixes:
+  - "docker_image, docker_image_push - adjust image push detection to Docker 29 (https://github.com/ansible-collections/community.docker/pull/1199)."
+known_issues:
+  - "docker_image, docker_image_export - idempotency for archiving images depends on whether the image IDs used by the image storage backend correspond to the IDs used in the tarball's ``manifest.json`` files.
+     The new default backend in Docker 29 apparently uses image IDs that no longer correspond, whence idempotency no longer works (https://github.com/ansible-collections/community.docker/pull/1199)."
diff --git a/plugins/modules/docker_image.py b/plugins/modules/docker_image.py
index dd17a6f4..89f9c7fc 100644
--- a/plugins/modules/docker_image.py
+++ b/plugins/modules/docker_image.py
@@ -22,6 +22,8 @@ description:
 notes:
   - Building images is done using Docker daemon's API. It is not possible to use BuildKit / buildx this way. Use M(community.docker.docker_image_build)
     to build images with BuildKit.
+  - Exporting images is generally not idempotent. It depends on whether the image ID equals the IDs found in the generated tarball's C(manifest.json).
+    This was the case with the default storage backend up to Docker 28, but seems to have changed in Docker 29.
 extends_documentation_fragment:
   - community.docker.docker.api_documentation
   - community.docker.attributes
@@ -735,7 +737,7 @@ class ImageManager(DockerBaseClass):
                         if line.get('errorDetail'):
                             raise Exception(line['errorDetail']['message'])
                         status = line.get('status')
-                        if status == 'Pushing':
+                        if status in ("Pushing", "Pushed"):
                             changed = True
                     self.results['changed'] = changed
                 except Exception as exc:
diff --git a/plugins/modules/docker_image_export.py b/plugins/modules/docker_image_export.py
index 23997f41..0ccf292b 100644
--- a/plugins/modules/docker_image_export.py
+++ b/plugins/modules/docker_image_export.py
@@ -29,7 +29,13 @@ attributes:
   diff_mode:
     support: none
   idempotent:
-    support: full
+    support: partial
+    details:
+      - Whether the module is idempotent depends on the storage API used for images,
+        which determines how the image ID is computed. The idempotency check needs
+        that the image ID equals the ID stored in archive's C(manifest.json).
+        This seemed to have worked fine with the default storage backend up to Docker 28,
+        but seems to have changed in Docker 29.
 
 options:
   names:
diff --git a/plugins/modules/docker_image_push.py b/plugins/modules/docker_image_push.py
index 89ba1e31..3825a910 100644
--- a/plugins/modules/docker_image_push.py
+++ b/plugins/modules/docker_image_push.py
@@ -161,7 +161,7 @@ class ImagePusher(DockerBaseClass):
                 if line.get('errorDetail'):
                     raise Exception(line['errorDetail']['message'])
                 status = line.get('status')
-                if status == 'Pushing':
+                if status in ("Pushing", "Pushed"):
                     results['changed'] = True
         except Exception as exc:
             if 'unauthorized' in str(exc):
diff --git a/plugins/modules/docker_image_remove.py b/plugins/modules/docker_image_remove.py
index 815355cf..180da327 100644
--- a/plugins/modules/docker_image_remove.py
+++ b/plugins/modules/docker_image_remove.py
@@ -210,6 +210,7 @@ class ImageRemover(DockerBaseClass):
 
         elif is_image_name_id(name):
             results['deleted'].append(image['Id'])
+            # TODO: the following is no longer correct with Docker 29+...
             results['untagged'] = sorted((image.get('RepoTags') or []) + (image.get('RepoDigests') or []))
             if not self.force and results['untagged']:
                 self.fail('Cannot delete image by ID that is still in use - use force=true')
diff --git a/tests/integration/targets/docker_image/tasks/tests/options.yml b/tests/integration/targets/docker_image/tasks/tests/options.yml
index b76e1a61..71768bc7 100644
--- a/tests/integration/targets/docker_image/tasks/tests/options.yml
+++ b/tests/integration/targets/docker_image/tasks/tests/options.yml
@@ -256,6 +256,10 @@
 - assert:
     that:
       - archive_image_2 is not changed
+  when: docker_cli_version is version("29.0.0", "<")
+  # Apparently idempotency no longer works with the default storage backend
+  # in Docker 29.0.0.
+  # https://github.com/ansible-collections/community.docker/pull/1199
 
 - name: Archive image 3rd time, should overwrite due to different id
   docker_image:
diff --git a/tests/integration/targets/docker_image_export/tasks/tests/basic.yml b/tests/integration/targets/docker_image_export/tasks/tests/basic.yml
index 653e459b..a55c98b5 100644
--- a/tests/integration/targets/docker_image_export/tasks/tests/basic.yml
+++ b/tests/integration/targets/docker_image_export/tasks/tests/basic.yml
@@ -67,3 +67,7 @@
         manifests_json: "{{ manifests.results | map(attribute='stdout') | map('from_json') }}"
         manifest_json_images: "{{ item.2 | map(attribute='Config') | map('regex_replace', '.json$', '') | map('regex_replace', '^blobs/sha256/', '') | sort }}"
         export_image_ids: "{{ item.1 | map('regex_replace', '^sha256:', '') | unique | sort }}"
+      when: docker_cli_version is version("29.0.0", "<")
+      # Apparently idempotency no longer works with the default storage backend
+      # in Docker 29.0.0.
+      # https://github.com/ansible-collections/community.docker/pull/1199
diff --git a/tests/integration/targets/docker_image_load/tasks/tests/basic.yml b/tests/integration/targets/docker_image_load/tasks/tests/basic.yml
index 1b1c04c6..0db6c3ce 100644
--- a/tests/integration/targets/docker_image_load/tasks/tests/basic.yml
+++ b/tests/integration/targets/docker_image_load/tasks/tests/basic.yml
@@ -73,11 +73,17 @@
   loop: "{{ all_images }}"
   when: remove_all_images is failed
 
+- name: Show all images
+  ansible.builtin.command: docker image ls
+
 - name: Load all images (IDs)
   docker_image_load:
     path: "{{ remote_tmp_dir }}/archive-2.tar"
   register: result
 
+- name: Show all images
+  ansible.builtin.command: docker image ls
+
 - name: Print loaded image names
   debug:
     var: result.image_names
@@ -110,11 +116,17 @@
     name: "{{ item }}"
   loop: "{{ all_images }}"
 
+- name: Show all images
+  ansible.builtin.command: docker image ls
+
 - name: Load all images (mixed images and IDs)
   docker_image_load:
     path: "{{ remote_tmp_dir }}/archive-3.tar"
   register: result
 
+- name: Show all images
+  ansible.builtin.command: docker image ls
+
 - name: Print loading log
   debug:
     var: result.stdout_lines
@@ -127,10 +139,14 @@
     that:
       - result is changed
       # For some reason, *sometimes* only the named image is found; in fact, in that case, the log only mentions that image and nothing else
-      - "result.images | length == 3 or ('Loaded image: ' ~ docker_test_image_hello_world) == result.stdout"
-      - (result.image_names | sort) in [[image_names[0], image_ids[0], image_ids[1]] | sort, [image_names[0]]]
-      - result.images | length in [1, 3]
-      - (result.images | map(attribute='Id') | sort) in [[image_ids[0], image_ids[0], image_ids[1]] | sort, [image_ids[0]]]
+      # With Docker 29, a third possibility appears: just two entries.
+      - >-
+        result.images | length == 3
+        or ('Loaded image: ' ~ docker_test_image_hello_world) == result.stdout
+        or result.images | length == 2
+      - (result.image_names | sort) in [[image_names[0], image_ids[0], image_ids[1]] | sort, [image_names[0], image_ids[1]] | sort, [image_names[0]]]
+      - result.images | length in [1, 2, 3]
+      - (result.images | map(attribute='Id') | sort) in [[image_ids[0], image_ids[0], image_ids[1]] | sort, [image_ids[0], image_ids[1]] | sort, [image_ids[0]]]
 
 # Same image twice
 
@@ -139,11 +155,17 @@
     name: "{{ item }}"
   loop: "{{ all_images }}"
 
+- name: Show all images
+  ansible.builtin.command: docker image ls
+
 - name: Load all images (same image twice)
   docker_image_load:
     path: "{{ remote_tmp_dir }}/archive-4.tar"
   register: result
 
+- name: Show all images
+  ansible.builtin.command: docker image ls
+
 - name: Print loaded image names
   debug:
     var: result.image_names
@@ -151,10 +173,11 @@
 - assert:
     that:
       - result is changed
-      - result.image_names | length == 1
-      - result.image_names[0] == image_names[0]
-      - result.images | length == 1
+      - result.image_names | length in [1, 2]
+      - (result.image_names | sort) in [[image_names[0]], [image_names[0], image_ids[0]] | sort]
+      - result.images | length in [1, 2]
       - result.images[0].Id == image_ids[0]
+      - result.images[1].Id | default(image_ids[0]) == image_ids[0]
 
 # Single image by ID
 
@@ -163,11 +186,17 @@
     name: "{{ item }}"
   loop: "{{ all_images }}"
 
+- name: Show all images
+  ansible.builtin.command: docker image ls
+
 - name: Load all images (single image by ID)
   docker_image_load:
     path: "{{ remote_tmp_dir }}/archive-5.tar"
   register: result
 
+- name: Show all images
+  ansible.builtin.command: docker image ls
+
 - name: Print loaded image names
   debug:
     var: result.image_names
@@ -197,11 +226,17 @@
     name: "{{ item }}"
   loop: "{{ all_images }}"
 
+- name: Show all images
+  ansible.builtin.command: docker image ls
+
 - name: Load all images (names)
   docker_image_load:
     path: "{{ remote_tmp_dir }}/archive-1.tar"
   register: result
 
+- name: Show all images
+  ansible.builtin.command: docker image ls
+
 - name: Print loaded image names
   debug:
     var: result.image_names
diff --git a/tests/integration/targets/docker_image_pull/tasks/tests/basic.yml b/tests/integration/targets/docker_image_pull/tasks/tests/basic.yml
index 998549e4..f7ae3b33 100644
--- a/tests/integration/targets/docker_image_pull/tasks/tests/basic.yml
+++ b/tests/integration/targets/docker_image_pull/tasks/tests/basic.yml
@@ -142,6 +142,8 @@
           - present_3_check.actions[0] == ('Pulled image ' ~ image_name)
           - present_3_check.diff.before.id == present_1.diff.after.id
           - present_3_check.diff.after.id == 'unknown'
+    - ansible.builtin.assert:
+        that:
           - present_3 is changed
           - present_3.actions | length == 1
           - present_3.actions[0] == ('Pulled image ' ~ image_name)
@@ -166,6 +168,11 @@
           - present_5.actions[0] == ('Pulled image ' ~ image_name)
           - present_5.diff.before.id == present_3.diff.after.id
           - present_5.diff.after.id == present_1.diff.after.id
+      when: docker_cli_version is version("29.0.0", "<")
+      # From Docker 29 on, Docker won't pull images for other architectures
+      # if there are better matching ones. The above tests assume it will
+      # just do what it is told, and thus fail from 29.0.0 on.
+      # https://github.com/ansible-collections/community.docker/pull/1199
 
   always:
     - name: cleanup
diff --git a/tests/integration/targets/docker_image_pull/tasks/tests/image-ids.yml b/tests/integration/targets/docker_image_pull/tasks/tests/image-ids.yml
index 77552943..61a4488d 100644
--- a/tests/integration/targets/docker_image_pull/tasks/tests/image-ids.yml
+++ b/tests/integration/targets/docker_image_pull/tasks/tests/image-ids.yml
@@ -7,11 +7,9 @@
   block:
     - name: Make sure images are not there
       docker_image_remove:
-        name: "{{ item }}"
+        name: "sha256:{{ item }}"
         force: true
-      loop:
-        - "sha256:{{ docker_test_image_digest_v1_image_id }}"
-        - "sha256:{{ docker_test_image_digest_v2_image_id }}"
+      loop: "{{ docker_test_image_digest_v1_image_ids + docker_test_image_digest_v2_image_ids }}"
 
     - name: Pull image 1
       docker_image_pull:
@@ -82,8 +80,6 @@
   always:
     - name: cleanup
       docker_image_remove:
-        name: "{{ item }}"
+        name: "sha256:{{ item }}"
         force: true
-      loop:
-        - "sha256:{{ docker_test_image_digest_v1_image_id }}"
-        - "sha256:{{ docker_test_image_digest_v2_image_id }}"
+      loop: "{{ docker_test_image_digest_v1_image_ids + docker_test_image_digest_v2_image_ids }}"
diff --git a/tests/integration/targets/docker_image_push/tasks/tests/basic.yml b/tests/integration/targets/docker_image_push/tasks/tests/basic.yml
index bbbfc551..978ac831 100644
--- a/tests/integration/targets/docker_image_push/tasks/tests/basic.yml
+++ b/tests/integration/targets/docker_image_push/tasks/tests/basic.yml
@@ -18,7 +18,7 @@
 
     - name: Push image ID (must fail)
       docker_image_push:
-        name: "sha256:{{ docker_test_image_digest_v1_image_id }}"
+        name: "sha256:{{ docker_test_image_digest_v1_image_ids[0] }}"
       register: fail_2
       ignore_errors: true
 
diff --git a/tests/integration/targets/docker_image_push/tasks/tests/registry.yml b/tests/integration/targets/docker_image_push/tasks/tests/registry.yml
index 4f15490d..cff9d794 100644
--- a/tests/integration/targets/docker_image_push/tasks/tests/registry.yml
+++ b/tests/integration/targets/docker_image_push/tasks/tests/registry.yml
@@ -80,4 +80,6 @@
             that:
               - push_4 is failed
               - >-
-                push_4.msg == ('Error pushing image ' ~ image_name_base2 ~ ':' ~ image_tag ~ ': no basic auth credentials')
+                push_4.msg.startswith('Error pushing image ' ~ image_name_base2 ~ ':' ~ image_tag ~ ': ')
+              - >-
+                push_4.msg.endswith(': no basic auth credentials')
diff --git a/tests/integration/targets/docker_image_remove/tasks/main.yml b/tests/integration/targets/docker_image_remove/tasks/main.yml
index 7643e3a3..53341149 100644
--- a/tests/integration/targets/docker_image_remove/tasks/main.yml
+++ b/tests/integration/targets/docker_image_remove/tasks/main.yml
@@ -8,15 +8,16 @@
 # and should not be used as examples of how to write Ansible roles #
 ####################################################################
 
-- block:
+- vars:
+    image: "{{ docker_test_image_hello_world }}"
+    image_ids: "{{ docker_test_image_hello_world_image_ids }}"
+  block:
     - name: Pick image prefix
       set_fact:
         iname_prefix: "{{ 'ansible-docker-test-%0x' % ((2**32) | random) }}"
 
     - name: Define image names
       set_fact:
-        image: "{{ docker_test_image_hello_world }}"
-        image_id: "{{ docker_test_image_hello_world_image_id }}"
         image_names:
           - "{{ iname_prefix }}-tagged-1:latest"
           - "{{ iname_prefix }}-tagged-1:foo"
@@ -24,8 +25,9 @@
 
     - name: Remove image complete
       docker_image_remove:
-        name: "{{ image_id }}"
+        name: "{{ item }}"
         force: true
+      loop: "{{ image_ids }}"
 
     - name: Remove tagged images
       docker_image_remove:
@@ -102,10 +104,11 @@
           - remove_2 is changed
           - remove_2.diff.before.id == pulled_image.image.Id
           - remove_2.diff.before.tags | length == 4
-          - remove_2.diff.before.digests | length == 1
+          # With Docker 29, there are now two digests in before and after:
+          - remove_2.diff.before.digests | length in [1, 2]
           - remove_2.diff.after.id == pulled_image.image.Id
           - remove_2.diff.after.tags | length == 3
-          - remove_2.diff.after.digests | length == 1
+          - remove_2.diff.after.digests | length in [1, 2]
           - remove_2.deleted | length == 0
           - remove_2.untagged | length == 1
           - remove_2.untagged[0] == (iname_prefix ~ '-tagged-1:latest')
@@ -174,10 +177,11 @@
           - remove_4 is changed
           - remove_4.diff.before.id == pulled_image.image.Id
           - remove_4.diff.before.tags | length == 3
-          - remove_4.diff.before.digests | length == 1
+          # With Docker 29, there are now two digests in before and after:
+          - remove_4.diff.before.digests | length in [1, 2]
           - remove_4.diff.after.id == pulled_image.image.Id
           - remove_4.diff.after.tags | length == 2
-          - remove_4.diff.after.digests | length == 1
+          - remove_4.diff.after.digests | length in [1, 2]
           - remove_4.deleted | length == 0
           - remove_4.untagged | length == 1
           - remove_4.untagged[0] == (iname_prefix ~ '-tagged-1:foo')
@@ -245,16 +249,22 @@
           - remove_6 is changed
           - remove_6.diff.before.id == pulled_image.image.Id
           - remove_6.diff.before.tags | length == 2
-          - remove_6.diff.before.digests | length == 1
+          # With Docker 29, there are now two digests in before and after:
+          - remove_6.diff.before.digests | length in [1, 2]
           - remove_6.diff.after.exists is false
-          - remove_6.deleted | length > 1
+          - remove_6.deleted | length >= 1
           - pulled_image.image.Id in remove_6.deleted
-          - remove_6.untagged | length == 3
+          - remove_6.untagged | length in [2, 3]
           - (iname_prefix ~ '-tagged-1:bar') in remove_6.untagged
           - image in remove_6.untagged
           - remove_6_check.deleted | length == 1
           - remove_6_check.deleted[0] == pulled_image.image.Id
-          - remove_6_check.untagged == remove_6.untagged
+          # The following is only true for Docker < 29...
+          # We use the CLI version as a proxy...
+          - >-
+            remove_6_check.untagged == remove_6.untagged
+            or
+            docker_cli_version is version("29.0.0", ">=")
           - info_5.images | length == 0
 
     - name: Remove image ID (force, idempotent, check mode)
diff --git a/tests/integration/targets/setup_docker/vars/main.yml b/tests/integration/targets/setup_docker/vars/main.yml
index 4fbb4496..97445dd4 100644
--- a/tests/integration/targets/setup_docker/vars/main.yml
+++ b/tests/integration/targets/setup_docker/vars/main.yml
@@ -4,12 +4,18 @@
 # SPDX-License-Identifier: GPL-3.0-or-later
 
 docker_test_image_digest_v1: e004c2cc521c95383aebb1fb5893719aa7a8eae2e7a71f316a4410784edb00a9
-docker_test_image_digest_v1_image_id: 758ec7f3a1ee85f8f08399b55641bfb13e8c1109287ddc5e22b68c3d653152ee
+docker_test_image_digest_v1_image_ids:
+  - 758ec7f3a1ee85f8f08399b55641bfb13e8c1109287ddc5e22b68c3d653152ee  # Docker 28 and before
+  - e004c2cc521c95383aebb1fb5893719aa7a8eae2e7a71f316a4410784edb00a9  # Docker 29
 docker_test_image_digest_v2: ee44b399df993016003bf5466bd3eeb221305e9d0fa831606bc7902d149c775b
-docker_test_image_digest_v2_image_id: dc3bacd8b5ea796cea5d6070c8f145df9076f26a6bc1c8981fd5b176d37de843
+docker_test_image_digest_v2_image_ids:
+  - dc3bacd8b5ea796cea5d6070c8f145df9076f26a6bc1c8981fd5b176d37de843  # Docker 28 and before
+  - ee44b399df993016003bf5466bd3eeb221305e9d0fa831606bc7902d149c775b  # Docker 29
 docker_test_image_digest_base: quay.io/ansible/docker-test-containers
 docker_test_image_hello_world: quay.io/ansible/docker-test-containers:hello-world
-docker_test_image_hello_world_image_id: sha256:bf756fb1ae65adf866bd8c456593cd24beb6a0a061dedf42b26a993176745f6b
+docker_test_image_hello_world_image_ids:
+  - sha256:bf756fb1ae65adf866bd8c456593cd24beb6a0a061dedf42b26a993176745f6b  # Docker 28 and before
+  - sha256:90659bf80b44ce6be8234e6ff90a1ac34acbeb826903b02cfa0da11c82cbc042  # Docker 29
 docker_test_image_hello_world_base: quay.io/ansible/docker-test-containers
 docker_test_image_busybox: quay.io/ansible/docker-test-containers:busybox
 docker_test_image_alpine: quay.io/ansible/docker-test-containers:alpine3.8
diff --git a/tests/integration/targets/setup_docker_registry/tasks/setup-frontend.yml b/tests/integration/targets/setup_docker_registry/tasks/setup-frontend.yml
index 2f2a500e..f439a3bb 100644
--- a/tests/integration/targets/setup_docker_registry/tasks/setup-frontend.yml
+++ b/tests/integration/targets/setup_docker_registry/tasks/setup-frontend.yml
@@ -102,7 +102,17 @@
         # This host/port combination cannot be used if the tests are running inside a docker container.
         docker_registry_frontend_address: localhost:{{ nginx_container.container.NetworkSettings.Ports['5000/tcp'].0.HostPort }}
         # The following host/port combination can be used from inside the docker container.
-        docker_registry_frontend_address_internal: "{{ nginx_container.container.NetworkSettings.Networks[current_container_network_ip].IPAddress if current_container_network_ip else nginx_container.container.NetworkSettings.IPAddress }}:5000"
+        docker_registry_frontend_address_internal: >-
+          {{
+            nginx_container.container.NetworkSettings.Networks[current_container_network_ip].IPAddress
+            if current_container_network_ip else
+            (
+              nginx_container.container.NetworkSettings.IPAddress
+              | default(nginx_container.container.NetworkSettings.Networks['bridge'].IPAddress)
+            )
+          }}:5000
+        # Since Docker 29, nginx_container.container.NetworkSettings.IPAddress no longer exists.
+        # Use the bridge network's IP address instead...
 
     - name: Wait for registry frontend
       uri:
diff --git a/tests/integration/targets/setup_openssl/tasks/main.yml b/tests/integration/targets/setup_openssl/tasks/main.yml
index b84159b7..2c72c9f0 100644
--- a/tests/integration/targets/setup_openssl/tasks/main.yml
+++ b/tests/integration/targets/setup_openssl/tasks/main.yml
@@ -27,7 +27,7 @@
 - name: Install cryptography (Darwin, and potentially upgrade for other OSes)
   become: true
   pip:
-    name: cryptography>=1.3.0
+    name: cryptography>=3.3.0
     extra_args: "-c {{ remote_constraints }}"
 
 - name: Register cryptography version