After several versions and iterations Docker have published a draft specification of the Docker Compose orchestration configuration files syntax. Compose enables developers and operators to specify complex container applications including storage and networking in a single YAML file.
Docker is working with AWS, Microsoft and others to extend the Compose Specification to support cloud-native platforms like Kubernetes and Amazon Elastic Container Service in addition to the existing Compose platforms. In addition to the Kompose tool that converts Compose configuration into Kubernetes resources there's also Compose on Kubernetes that can deploy complex container applications specified with Compose files to Kubernetes clusters.
There's a new homepage https://www.compose-spec.io/ that has various resources on Docker Compose and links to the specification on GitHub.