I will show that numerical investigations of a many-body ground state wavefunction using
the density matrix renormalization group (DMRG) method can yield a remarkably complete
characterization of different types of topological orders. A central tool is the entanglement
which encodes many of the essential features. First, I will show how characteristic properties of
the topological excitations in fractional quantum Hall states can be extracted directly from the
ground state wave function. Second, I will consider symmetry protected topological phases for
which the characterizing symmetry fractionalization can be determined.