  In this review article, we give overview on the extended chiral quark models.
In particular, how these models are extended to include the higher-order
interactions, quantized fields, logarithmic potential and the effect of these
modifications on hadron properties at hot and dense mediums. In addition, how
we deal with non-normalization of the Nambu-Jona-Lasinio (NJL) model by using
mid-point technique. Therefore, the extended quark models give satisfied
results in comparison with lattice QCD at finite temperature and baryonic
chemical potential. The extra effort is needed to deal with chiral quark models
in the presence of external magnetic field at finite temperature and density.
