Mozilla recently announced its new WebExtensions API. The API was created to streamline the creation of Web extensions for Firefox. Mozilla readily gives credit to Google Chrome extension APIs as the inspiration for the new Mozilla API, and hopes that the new API will become standardized.
Mozilla has published a number of resources to assist those interest with using the WebExtensions API. Check out the docs on MDN. Learn about the benefits of WebExtensions on the Mozilla Add-ons Blog. To get started, read through the MDN tutorial. A web-ext CLI tool is available for developers using command line. You can also test existing Chrome extensions in Firefox if interested.