Custom middleware in ASP.NET Core allows you to add your own logic to the request pipeline. To implement custom middleware, you need to create a class that has a method accepting a RequestDelegate parameter. In this method, you can write code to handle the incoming request, perform operations, and optionally invoke the next middleware in the pipeline. Custom middleware can be added to the pipeline using the UseMiddleware extension method in the Configure method of the Startup class. This gives you the flexibility to add custom functionality at various stages of the request processing pipeline.