Heegaard Floer homology can be used to define an invariant for knots in the three-sphere. This invariant, whose definition involves holomorphic curves, admits an elementary, combinatorial description in terms of grid diagrams. I will describe the construction, and sketch a combinatorial proof of its topological invariance. This lecture will cover joint work with Ciprian Manolescu, Sucharit Sarkar, Zoltán Szabó, and Dylan Thurston.