Heegaard Floer homology is an invariant for knots and three-manifolds defined using methods from Lagrangian Floer homology and symplectic geometry. I will describe a concrete model for computing this invariant for knots in S3. Time permitting, I will turn to some further developments in the theory. The material I will describe is joint with collaborators, including Robert Lipshitz, Ciprian Manolescu, Dylan Thurston, and Zoltán Szabó.