  Motivated by the potential applications of their intrinsic cross-coupling
properties, the interest in multiferroic materials has constantly increased
recently, leading to significant experimental and theoretical advancements.
From the theoretical point of view, recent progresses have allowed to identify
different mechanisms responsible for the appearence of ferroelectric
polarization coexisting with -- and coupled to -- magnetic properties. This
chapter aims at reviewing the fundamental mechanisms devised so far, mainly in
transition-metal oxides, which lie at the origin of multiferroicity.
