Critical behavior and net-charge fluctuations from lattice QCD

We present recent results on the critical and pseudo-critical temperatures in (2+1)-flavor QCD with a physical strange quark mass and two degenerate light quark masses extrapolated to the chiral limit and tuned to the physical value, respectively. We furthermore discuss implication of the observed low chiral phase transition temperature, Tc0=132_{-6}^{+3} MeV, for the structure of cumulants of conserved charge fluctuations at vanishing baryon chemical potential and consequences for the possible location of the QCD critical endpoint in the QCD phase diagram at non-zero baryon chemical potential.