Abstract: The Jones polynomial is a powerful polynomial knot invariant which was discovered in the early 1980s. In the late 1980s, Reshetikhin-Turaev showed that the Jones polynomial fits into a family of knot invariants coming from representation theory. Recently, Khovanov enhanced the Jones polynomial to a homology theory. After explaining these theories, I will explain a construction (joint with Sabin Cautis) of Khovanov homology using derived categories of coherent sheaves on certain varieties arising in the geometric Langlands program.