  At high density, matter is expected to undergo a phase transition to
deconfined quark matter. Although the density at which it happens and the
strength of the transition are still largely unknown, we can model it to be in
agreement with known experimental data and reliable theoretical results. We
discuss how deconfinement in dense matter can be affected by both by
temperature and by strong magnetic fields within the CMF model. To explore
different dependencies in our approach, we also explore how deconfinement can
be affected by the assumption of different degrees of freedom, different vector
coupling terms, and different deconfining potentials, all at zero temperature.
Both zero-net-strangeness and isospin-symmetric heavy-ion collision matter and
beta-equilibrated charge-neutral matter in neutron stars are discussed.
