The Density Matrix Renormalization Group is a new technique in quantum chemistry that is enabling the solution of many problems of electronic structure previously thought impossible. In my talk I will explain the basic idea behind the method and give many examples of classes of calculations, ranging from exact small molecule potential energy curves to excited states of conjugated polymers, that can now be performed using this theory. In addition, I will explain the connection between the Density Matrix Renormalization Group and the emerging paradigm of Tensor Network wavefunctions, which appear to underlie all computationally tractable strongly interacting systems.