Khovanov homology and knot Floer homology are two powerful link invariants with many similarities despite their seemingly unrelated constructions. In 2005, Rasmussen conjectured that there is a spectral sequence from Khovanov homology to knot Floer homology, which would explain many of these similarities. I will discuss a proof of this conjecture, as well as a construction for tangles that relates a bordered theory for Khovanov homology to the recent bordered knot Floer invariant of Ozsvath and Szabo. This is joint work with Akram Alishahi.