We are using Ivy with Artifactory as a repository. In Artifactory both third-party libraries and our release packages are stored.
If there is a bug in an artefact (3rd party or our package) I would like to find out which other components are potentially impacted.
In short, I need a reverse dependency report.
How similar problems are usually solved?
Check out Artifactory's build integration and CI server plugins.
The plugins collect information during build time (Both CI server and build tool), manage the deployment of artifacts and finally publish a "Build Info" report containing details regarding the build environment, method, dependencies and published artifacts.
Once in Artifactory, you can view a low down of each build with links to all produced artifacts, dependencies (if they exist in the repository) and even third-party license detection.
This will be helpful in your case, since you can also view all the builds an artifact was involved in, whether as a product or a dependency.
Artifactory's tree browser can display all the builds an artifact was involved in and it applies to all artifacts, not only build products; see the screenshot in this section as an example.
Artifactory's also got a REST resource that lets you query for builds in which a certain artifact has acted as a dependency; like the tree browser viewer, this too applies to all artifacts.
Currently, plugins are available for Jenkins, TeamCity and Bamboo and they all support Maven, Ivy and Gradle builds.