Kronheimer, Mrowka, Ozsváth, and Szabó obtained a new proof of Gordon and Luecke's Knot Complement Theorem using monopole Floer homology. That's pretty good, I think. They also proved that $\mathbb{RP}^3$ can't be obtained by surgery on a nontrivial knot (I don't know if there are any other proofs now).
Kronheimer, Mrowka, Ozsváth, Szabó, Monopoles and lens space surgeries. Ann. of Math. (2) 165 (2007), no. 2, 457–546.