Previously known as Swagger, the latest standard is OpenAPI 3, details on this can be found at Home - OpenAPI Initiative. It is worth noting that a lot of people still refer to this as Swagger. Originally the standard was developed by Software Testing, Monitoring, Developer Tools | SmartBear and up to and including version 2 of the standard it is Swagger, but in 2015 they donated everything to the OpenAPI Initiative under the Linux Foundation.

There is some good OpenAPI 3 documentation About Swagger Specification | Documentation | Swagger which I find easy to read.

There is a very good OpenAPI Generator which will generate client or server code to work with an API defined in a YAML or JSON file.

See also REST