Until recently, the von Neumann entropy and its generalizations (Renyi) were the principal quantitative characterizations of entanglement. A richer characterization, first developed here at Princeton, is becoming the tool of choice for investigating topological (and conventional) order in quantum ground states of condensed matter systems. A Schmidt decomposition that partitions the ground state between two sets of degrees of freedom can be presented as the spectrum of the reduced density matrix, characterized by symmetry quantum numbers, analogous to the spectrum of elementary excitations of a Hamiltonian. From this spectrum, a rich amount of information about the ground state, both topological and geometrical, can be extracted.