Response formatting and content negotiation allow your Web API to return data in different formats based on the client's preferences. In ASP.NET Core Web API, you can implement response formatting and content negotiation by using the MediaTypeFormatter and the Produces attribute. The MediaTypeFormatter determines the format of the response based on the request's Accept header or other factors. The Produces attribute allows you to specify the supported media types for an action or controller. By supporting multiple media types, such as JSON, XML, or others, you enable clients to request the format they prefer.