[Maarten88]

A racing surfkite like this one [1] has no problem going upwind really fast.

[1] https://www.youtube.com/watch?v=ltDLsumdXLA

[Sharlin]

I understand how sailing upwind works with a bermuda rig, but how do you do that with a kite, aerodynamically speaking?

[mushtar]

It works the same way, the kite acts like a wing and provides pull and something (kiteboard, fins, hydrofoil, etc.) resists that pull and provides a perpendicular force to the force from the kite power line.