Tampermonkey is the most popular userscript manager, with over 10 million weekly users. It's available for Chrome, Microsoft Edge, Safari, Opera Next and Firefox.
Tampermonkey makes it very easy to manage your userscripts and provides features like a clear overview over the running scripts, a built-in editor, ZIP-based import and export (Google Drive, Dropbox, OneDrive), automatic update checks and also browser and cloud storage based synchronization. And finally it's compatible to Greasemonkey up to version 3.x with experimental 4.x support.
Note: If you want to install the more often updated BETA version, then you can get it from here: https://tampermonkey.net/?browser=firefox