To implement a REST API in Elixir, use the Phoenix framework, which provides routing, controllers, and views. Define routes in router.ex and create controllers to handle requests and responses.

Implementing a REST API in Elixir is efficiently accomplished using the Phoenix framework, which is built on top of Elixir and designed for high-performance web applications. The first step is to create a new Phoenix project using the command mix phx.new my_api, which sets up the necessary directory structure and files. The router.ex file is where you define the routes for your API, mapping HTTP verbs (GET, POST, PUT, DELETE) to specific controller actions. For example, you might define a route for fetching a resource with get "/api/resources", ResourceController, :index. Each route points to a controller, where you implement the logic to handle incoming requests. Controllers can respond with JSON data using the json/2 function, making it easy to return structured responses. Additionally, you can leverage Ecto for database interactions to manage your data models efficiently. For better organization, consider creating contexts that encapsulate business logic and data access. By following RESTful principles, such as using appropriate status codes and resource naming conventions, you can create a well-structured API. By combining Phoenix with Ecto and organizing your code effectively, you can implement a robust REST API in Elixir that is easy to maintain and extend.