Biclique attack
A 2011 attack that gave the first result against full AES faster than brute force, if only by a small margin.
Andrey Bogdanov, Dmitry Khovratovich and Christian Rechberger showed that full AES-128 can be attacked with a technique based on bicliques in the key space, combined with meet-in-the-middle ideas. The complexity is roughly 2^126 operations: a little faster than brute force, and nowhere near practical.
It does not break AES in real use, but it is a reminder that security margins are not infinite.