  This is a survey article about knot Floer homology. We present three
constructions of this invariant: the original one using holomorphic disks, a
combinatorial description using grid diagrams, and a combinatorial description
in terms of the cube of resolutions. We discuss the geometric information
carried by knot Floer homology, and the connection to three- and
four-dimensional topology via surgery formulas. We also describe some
conjectural relations to Khovanov-Rozansky homology.
