  Some of the advances made in the literature to understand the phase
transitions of quark matter in the presence of strong magnetic field and finite
temperature (zero quark chemical potential) are reviewed. We start by
discussing the physics behind the Magnetic catalysis (MC) at zero/finite
temperature and then focus on the lattice predictions for inverse magnetic
catalysis (IMC) at high temperature and strong magnetic fields. Possible
explanations for the IMC are covered as well. Finally, we discuss recent
efforts to modify QCD (quantum chromodynamics) effective models in order to
reproduce the IMC observed on the lattice simulations. We emphasize the fact
that applying thermo-magnetic effects on the coupling constant of the NJL model
significantly improve the effectiveness of the NJL model to obtain a reasonable
physical description of hot and magnetized quark matter being in agreement with
lattice results.
