Given a ground-state wavefunction, how much can we tell about the system which it describes? Can we extract information about the excitations of a system directly from its ground-state? In topologically-ordered phases, recent progress shows that a new type of spectra, based on entanglement and not energy, can give a rather complete picture both of the counting of excitations as well as their wavefunctions. In the Fractional Quantum Hall effect, different types of partitioning the system in two different entangled parts reveal that the information about both edge and bulk excitations is encoded in the ground-state wavefunction. I will present strong evidence for a relationship between the entanglement spectra and the energy spectra which allows us to conjecture a new principle of adiabatic continuity based only on the ground-state wavefunction. I will also show that the entanglement spectra can also reveal new physics in topological insulators which is not readily available from the energy spectra.