I will present a combinatorial description of the Heegaard Floer invariants of three- and four-manifolds (mod 2). The idea is to represent the manifolds in terms of links in S3, and then to use grid diagrams to represent the links. Counting holomorphic polygons in symmetric products boils down to counting certain domains on the grids. This is based on joint work with P. Ozsvath and D. Thurston.