Elixir manages dependencies using the Mix tool, where you specify libraries in the `mix.exs` file and use commands to fetch and update them.

Dependency management in Elixir is primarily handled through the Mix build tool, which simplifies the process of adding, updating, and managing external libraries. To include a dependency in your Elixir project, you specify it in the deps function within your mix.exs file. For example, you can add a dependency like {:httpoison, "~> 1.8"} to fetch the HTTP client library. After updating your mix.exs, you run mix deps.get to fetch and install the specified libraries. Mix also allows for version constraints, enabling you to control which versions of a library your project can use, thus ensuring stability and compatibility. You can check for outdated dependencies with mix deps.outdated and update them using mix deps.update. This integrated dependency management system makes it easy for Elixir developers to maintain their projects and leverage a wide range of libraries and frameworks effectively.