The aim of this work is to provide an overview over recent advances in the simulation algorithms for quantum many body problems.We focus on the class of algorithms that are based on the density matrix renormalization group.In this work we will outline the density matrix renormalization group based approach to simulating quantum many body problems and the proposals to generalize the density matrix renormalization group to two or higher dimensional problems. A special focus is on the generalization of DMRG to tree tensor networks.