Webstorm 7 cannot recognize node API methods

For 2018 and later versions of WebStorm:

In Settings -> Languages & Frameworks -> Node.js and NPM, check Coding assistance for Node.js:

_{In older Webstorm versions, this was called Enable Node.js Core library.}

If you still see unrecognized Node symbols even with that option enabled, unckeck it, restart WebStorm, then right click on the warning and choose Enable Node.js coding assistance or just check the option again. Watch for WebStorm to show it's Indexing files. (Just had this happen today - looks like a WebStorm bug, and what I just wrote fixed the situation.)

For WebStorm 7 thru 10 (on OSX)…

WebStorm → Preferences → Languages & Frameworks → Javascript → Libraries

Select "Node.js Globals" and "Node.js vXXX Core Modules".