  I review recent results obtained within chiral effective models, on the phase
structure of hot quark matter in a strong magnetic background. After a brief
introduction, I focus on the results obtained within two chiral models improved
with the Polyakov loop. The models differ for the content of interactions, but
both of them are tuned to reproduce Lattice QCD thermodynamics at zero and
imaginary chemical potential. One of them takes into account an explicit
Polyakov loop dependence of the coupling; the other one neglects this
contribution, but takes into account multi-quark interactions. A comparison
between the phase diagrams of the two models is presented.
