The DMRG has been successfully applied to get the low energy properties of spin chains: Ising model in a transverse field, Heisenberg model, etc., fermionic systems, such as the Hubbard model, problems with impurities such as the Kondo effect, boson systems, and the physics of quantum dots joined with quantum wires. It has been also extended to work on tree graphs, and has found applications in the study of dendrimers. For 2D systems with one of the dimensions much larger than the other DMRG is also accurate, and has proved useful in the study of ladders.