The term superfrustration refers to massive ground state degeneracy in supersymmetric lattice models for itinerant fermions with strong repulsive interactions, in dimension D>1. In general, quantum phases of lattice fermions are hard to track, due to lack of analytic methods and fundamental difficulties in numerical analysis. I will show how supersymmetry improves this situation and leads to exact results on the number and nature of quantum gound states. Superfrustration is established by showing that on a variety of 2D lattices the supersymmetric model has extensive ground state entropy. For the 2D square lattice I demonstrate the existence of critical edge excitations.