  We study the behavior of strongly interacting matter under a strong external
magnetic field in the context of chiral quark models that include nonlocal
interactions. In particular, we analyze the influence of a constant magnetic
field on the chiral quark condensates at zero and finite temperature, studying
the deconfinement and chiral restoration critical temperatures and discussing
the observed "magnetic catalysis" and "inverse magnetic catalysis" effects. In
addition, we analyze in this framework the behavior of the $\pi^0$ mass and
decay constant. The predictions of nonlocal chiral quark models are compared
with results obtained in lattice QCD.
