Dependencies in Elixir are managed through the Mix build tool by specifying them in the `mix.exs` file. You can fetch and update dependencies using Mix commands.

Managing dependencies in Elixir is straightforward thanks to the Mix build tool, which provides a structured way to declare and handle external libraries your project relies on. To add a dependency, you specify it in the deps/0 function within your project's mix.exs file. Each dependency is defined with its name and version constraints, enabling you to control which versions of the libraries are used in your project. For example, you might add a dependency like this: {:some_library, "~> 2.0"}. Once you have updated the mix.exs file, you can run the command mix deps.get to fetch and install the specified dependencies. Mix also allows you to manage dependencies easily by updating them with mix deps.update some_library, ensuring your project remains up-to-date with the latest features and bug fixes. Additionally, Mix provides a built-in task to check for outdated dependencies using mix deps.outdated. By leveraging Mix for dependency management, Elixir developers can ensure their projects are stable, maintainable, and equipped with the necessary libraries to build robust applications.