  We study the behavior of strongly interacting matter under a uniform intense
external magnetic field in the context of nonlocal extensions of the
Polyakov-Nambu-Jona-Lasinio model. A detailed description of the formalism is
presented, considering the cases of zero and finite temperature. In particular,
we analyze the effect of the magnetic field on the chiral restoration and
deconfinement transitions, which are found to occur at approximately the same
critical temperatures. Our results show that these models offer a natural
framework to account for the phenomenon of inverse magnetic catalysis found in
lattice QCD calculations.
