In my presentation I will describe the numerical methods to determine both Abelian and non-Abelian topological order starting from a lattice Hamiltonian. The key idea is to find the topological S and T matrices, which (in most known cases) can be considered as a nonlocal order parameter of topologically ordered phases, in the sense that they give us unambiguous information about the model along with its excitations and their statistics. With the PEPS, the method allows to analyze states which were not achievable by the state-of-the-art 2D DMRG algorithms due to long correlation length and it is immune to any small perturbations of the tensors, which had been a long feared problem due to numerical inaccuracies which may arise during the ground state optimization. Furthermore this construction enables an elegant description of the model in terms of the mathematical structure underlying the topologically ordered phases of matter - modular tensor category.s