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Heegaard Floer homology is a homological invariant of 3-manifolds and knots whose Euler characteristic is the Alexander polynomial. It detects knot genus (or more generally the Thurston norm) and fibration, and has many other uses. There is an elegant combinatorial formulation of knot Heegaard Floer homology from grid diagrams, a grown-up version of tic-tac-toe. After reviewing this construction, we then use grid diagrams to motivate an extension of the theory to 3-manifolds with parametrized boundary. This is joint work with Robert Lipshitz and Peter Ozsváth.