I will give an overview over my results on the description of many-body localized (MBL) systems with quantum circuits – a specific type of tensor networks. I will present how they can be used numerically to simulate the MBL-to-thermal transition observed in two-dimensional optical lattice experiments. I obtained a transition point consistent with the latest charge-density wave experiments and was also able to extract the mobility edge. I will explain why this description captures experimentally relevant time scales on which two-dimensional MBL is visible. I will also indicate how quantum circuits can be used to rigorously classify symmetry-protected topological MBL phases in one and two dimensions. Finally, I will demonstrate that the conventional notion of local integrals of motion has to be revised for topologically ordered MBL systems. I will argue that all of their eigenstates must have the same topological order, which cannot change unless sufficiently strong perturbations destroy MBL.