The OpenAPI Specification is becoming a broadly adopted industry standard for describing modern REST APIs. Other initiatives like RAML have joined the OpenAPI Initiative.
OpenAPI v2 version is basically the former Swagger - and Swagger provides useful tools for OpenAPI like the online editor and viewer http://editor.swagger.io/ We have also found that this version currently have a good tool support accross languages, so you will find API client and server generation tools for a lot of languages, which makes it quite easy to connect to an API that is described in OpenAPI standard.
OpenAPI v3 adds more features to the specification - for example the ability to describe APIs supporting request/callback pattern.
The general tool support is excellent. See https://openapi.tools/