  We study two effective models for QCD, the Nambu-Jona-Lasinio -model and the
linear sigma model extended by including a Polyakov loop potential, which is
fitted to reproduce pure gauge theory thermodynamics, and a coupling between
the chiral fields and the Polyakov loop. Thus the resulting models have as
relevant degrees of freedom the Polyakov loop and chiral fields. By comparing
the extended models with the bare chiral models we can conclude that the
addition of the Polyakov loop is necessary in order to obtain both
qualitatively and quantitatively correct results at finite temperatures. These
results are extended to finite net quark densities, several thermodynamical
quantites are investigated in detail and possible applications and consequences
for relativistic heavy ion collision phenomenology are discussed.
