  We review the main features of the QCD phase diagram description, at finite
temperature, baryon density and in the presence of a magnetic field, from the
point of view of effective models, whose main ingredient is chiral symmetry. We
concentrate our attention on two of these models: The linear sigma model with
quarks and the Nambu--Jona-Lasinio model. We show that a main ingredient to
understand the characteristics of the phase transitions is the inclusion of
plasma screening effects that capture the physics of collective, long-wave
modes, and thus describe a prime property of plasmas near transition lines,
namely, long distance correlations. Inclusion of plasma screening makes
possible to understand the inverse magnetic catalysis phenomenon even without
the need to consider magnetic field-dependent coupling constants. Screening is
also responsible for the emergence of a critical end point in the phase diagram
even for small magnetic field strengths. Although versatile, the NJL model is
also a more limited approach since, being a non-renormalizable model, a clear
separation between pure vacuum and medium effects is not always possible. The
model cannot describe inverse magnetic catalysis unless a magnetic field
dependent coupling is included. The location of the critical end point strongly
depends on the choice of the type of interaction and on the magnetic field
dependence of the corresponding coupling. Overall, both models provide sensible
tools to explore the properties of magnetized, strongly interacting matter.
However, a cross talk among them as well as a consistent physical approach to
determine the model parameters is much needed.
