The document discusses different patterns for using an API gateway, including: 1) API management for existing APIs to handle cross-cutting concerns in one place 2) Ingress for APIs and services to manage traffic entering a cluster 3) Application modernization to help split a monolith into microservices gradually 4) Simplified aggregated API to simplify access to multiple complex internal services 5) Using a service mesh for internal east-west traffic between services while using a gateway for north-south external traffic The document provides examples and use cases for each pattern and concludes that the right approach depends on specific needs, and that gateways and service meshes can overlap on common concerns like security and observability.