In CSS, FontAwesome unicode works only when the correct font family is declared (version 4 or less):
font-family: "FontAwesome";
content: "\f066";
Update - Version 5 has different names:
Free
font-family: "Font Awesome 5 Free"
Pro
font-family: "Font Awesome 5 Pro"
Brands
font-family: "Font Awesome 5 Brands"
See this related answer: https://stackoverflow.com/a/48004111/2575724
As per comment (BuddyZ) some more info here https://fontawesome.com/how-to-use/on-the-desktop/setup/getting-started