Fae don't seem to feature much in Dungeons and Dragons games (that I have played) and I think it's probably because they're low challenge in combat. But why would faeries, who are essentially physically weak extradimensional magic users, be interested in engaging in combat when they could be playing to their strengths?
By their nature, the Fair Folk are otherworldly, capricious, playful, powerful, and broadly disinterested in us and our world unless they can derive some entertainment or gain.
Here are my thoughts on how to take advantage of this nature to have fun at the table: