  We summarize recent results obtained in the Dyson-Schwinger formalism to
study the chiral and deconfinement phase transitions of quenched and unquenched
QCD at finite temperature and chemical potential. In the quenched case we
compare SU(2) and SU(3) gauge theories by taking lattice data for the gluon as
an input for the quark Dyson-Schwinger equation. As compared to previous
investigations we find a clearer distinction between the second order
transition of the two-color theory and the (weak) first order transition of the
three-color gauge theory. We then extend this study to unquenched QCD at finite
chemical potential by taking matter effects to the gluon into account and
investigate the order of the chiral phase transition and the behavior of the
deconfinement transition. What we find are coinciding phase transitions up to a
critical endpoint which is located at large chemical potential.
