  We study consistently the effects of magnetic field on hot and dense matter.
In particular, we look for differences that arise due to assumptions that
reproduce the conditions produced in particle collisions or astrophysical
scenarios, such as in the core of fully evolved neutron stars (beyond the
protoneutron star stage). We assume the magnetic field to be either constant or
follow a profile extracted from general relativity calculations of magnetars
and make use of two realistic models that can consistently describe chiral
symmetry restoration and deconfinement to quark matter, the Chiral Mean Field
(CMF) and the Polyakov-loop extended Nambu-Jona-Lasinio (PNJL) models. We find
that net isospin, net strangeness, and weak chemical equilibrium with leptons
can considerably change the effects of temperature and magnetic fields on
particle content and deconfinement in dense matter. We finish by discussing the
possibility of experimentally detecting quark deconfinement in dense and/or hot
matter and the possible role played by magnetic fields.
