The primary characteristics of a RESTful API include statelessness, resource orientation, and the use of standard HTTP methods. REST (Representational State Transfer) principles promote a design where each API call is independent and does not rely on previous calls, enhancing scalability and performance. RESTful APIs utilize standard operations like GET, POST, PUT, and DELETE for resource manipulation, operating over URI endpoints. Additionally, they typically return data in formats like JSON or XML, facilitating interoperability and ease of integration across different platforms and applications.