  The understanding of the behaviour of strongly interacting matter at finite
temperature and density is of fundamental interest and has applications in
cosmology, in the astrophysics of neutron stars and in the physics of
relativistic heavy ion collisions. Given the possible existence of strong
magnetic fields in the mentioned situations, their effect on the QCD phase
diagram has recently become a topic of increasing interest. Here, we report on
the study of this issue in the framework of the two flavor Nambu-Jona-Lasinio
model with Polyakov loop (PNJL) and an extension of it, the so-called entangled
PNJL model (EPNJL).
