Inverse magnetic catalysis: how much do we know about?

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 to reproduce the IMC observed on the lattice simulations. We emphasize the fact that applying thermomagnetic 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.