Approaching the QCD phase diagram for N_f=2+1 and N_f=2+1+1 quark flavors

Recent results for the QCD phase structure at finite temperature and light-quark chemical potential are summarized, where the cases of N_f = 2 + 1 and N_f = 2+1+1 dynamical quark flavors are considered. Order parameters for the chiral and deconfinement transitions are obtained from solutions of a coupled set of truncated Dyson-Schwinger equations for the quark and gluon propagators of Landau gauge QCD. Based on very good agreement with lattice QCD for zero chemical potential the phase diagram in the whole T-\mu-plane and the appearance of a putative critical end-point at large chemical potential are studied.