API gateways serve as a crucial component in a microservices architecture by providing a single entry point for client requests. Their primary advantage lies in request routing, enabling the routing of requests to appropriate services, thus simplifying client interactions. Additionally, API gateways offer features like authentication, load balancing, logging, and rate limiting, enhancing security and performance. By managing these concerns centrally, they reduce the complexity of individual microservices, enabling developers to focus on service functionality rather than communication overhead.