Custom middleware allows you to add additional behavior or processing to the request pipeline of your Web API. In ASP.NET Core, you can implement custom middleware by creating a class that follows the middleware convention. The middleware class should have a constructor that takes a RequestDelegate parameter and an InvokeAsync method that handles the request and optionally calls the next middleware in the pipeline. By configuring and registering your custom middleware in the Startup class, you can add custom processing, logging, authentication, or any other behavior to the request pipeline of your Web API.