  The key physical property of multiferroic materials is the existence of a
coupling between magnetism and polarization, i.e. magnetoelectricity. The
origin and manifestations of magnetoelectricity can be very different in the
available plethora of multiferroic systems, with multiple possible mechanisms
hidden behind the phenomena. In this Review, we describe the fundamental
physics that causes magnetoelectricity from a theoretical viewpoint. The
present review will focus on the main stream physical mechanisms in both single
phase multiferroics and magnetoelectric heterostructures. The most recent
tendencies addressing possible new magnetoelectric mechanisms will also be
briefly outlined.
