The Kubernetes API is comprehensive and encompasses the entire functionality of Kubernetes. As you may expect, it is huge. But it is designed very well using best practices, and it is consistent. If you understand the basic principles, you can discover everything you need to know.
Working with the Kubernetes API
Understanding OpenAPI
OpenAPI allows API providers to define their operations and models, and enables developers to automate their tools and generate their favorite language's client to talk to that API server. Kubernetes has supported Swagger 1.2 (an older version of the OpenAPI spec) for a while, but the spec was incomplete and invalid, making it hard to generate tools/clients based on it.
In Kubernetes 1.4...