The density matrix renormalization group is the most successful numerical approach for finding ground states of one dimensional systems in condensed matter physics. We now understand that DMRG is based on a natural low-entanglement approximation, exploiting the low entanglement of ground states embodied in the area law for entanglement entropy. DMRG has gradually become a leading technique for studying two dimensional systems, particularly frustrated magnetic systems, where much effort has gone into the search for realistic models which can be shown to have quantum spin liquid ground states. In this talk, I will give a broad overview of DMRG and quantum spin liquids, our recent success in showing that the Kagome lattice Heisenberg model is a spin liquid, and our attempts to find additional spin liquid models.