  We initiate a systematic study of entanglement and Renyi entropies in the
presence of gauge and gravitational anomalies in even-dimensional quantum field
theories. We argue that the mixed and gravitational anomalies are sensitive to
boosts and obtain a closed form expression for their behavior under such
transformations. Explicit constructions exhibiting the dependence of
entanglement entropy on boosts is provided for theories on spacetimes with
non-trivial magnetic fluxes and (or) non-vanishing Pontryagin classes.
