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We study the behavior of strongly interacting matter under a strong externalmagnetic field in the context of chiral quark models that include nonlocalinteractions. In particular, we analyze the influence of a constant magneticfield on the chiral quark condensates at zero and finite temperature, studyingthe deconfinement and chiral restoration critical temperatures and discussingthe observed "magnetic catalysis" and "inverse magnetic catalysis" effects. Inaddition, we analyze in this framework the behavior of the $\pi^0$ mass anddecay constant. The predictions of nonlocal chiral quark models are comparedwith results obtained in lattice QCD.

Effects of strong magnetic fields on quark matter and $\pi^0$ properties within nonlocal chiral quark models