On MacOSX (as for September 11, 2017)
Key Command
⌘K ⌘C Add Line Comment
⌘K ⌘U Remove Line Comment
⌘/ Toggle Line Comment
⇧⌥A Toggle Block Comment
On Linux (tested on Ubuntu)
Key Command
Ctrl+/ Toggle Line Comment
Ctrl+Shift+A Toggle Block Comment
Credits: https://stackoverflow.com/questions/34316156/how-to-comment-multiple-lines-in-visual-studio-code#34317039