The entanglement spectrum, i.e. the logarithm of the eigenvalues of reduced density matrices of
quantum many body wave functions, has been the focus of a rapidly expanding research endeavor recently.
Initially introduced by Li & Haldane in the context of the fractional quantum Hall effect, its usefulness has been
shown to extend to many more fields, such as topological insulators, fractional Chern insulators, spin liquids,
continuous symmetry breaking states, etc.
After a general introduction to the field we review some of our own contributions to the field, in particular the
perturbative structure of the entanglement spectrum in gapped phases, the entanglement spectrum across the
Mott-insulator transition in the Bose-Hubbard model, and the relation of the entanglement spectrum of
(1+1) dimensional quantum critical systems to the operator content of their underlying CFT.