Abstract:  The density-matrix renormalization group (DMRG), based on matrix product states (MPS), is arguably the most successful group of algorithms in the tensor network framework and has established itself as the leading method for one-dimensional model Hamiltonians in equilibrium and to a large extent also out of equilibrium. The question is, of course, can we go beyond that? In this talk, I want to review progress made in the development of time-dependent simulations over the last few years, and show how it has been instrumental in allowing powerful applications in the field of more realistic material simulations for correlated matter when combined with the dynamical mean-field theory (DMFT). Finally, I want to show how automated modifications of the underlying single-particle bases allow much more powerful simulations for two-dimensional model Hamiltonians such as the Hubbard model, a development which is still in its early stages.