Selected topics on the QCD phase diagram at finite temperature and density

We will report recent progress on the QCD phase diagram at finite temperature and density. In particular, we discuss the universal scaling of the chiral transition in the limit of two massless quarks and one strange quark. We also discuss influence of other control parameter as chemical potentials, external magnetic field strength and number of quark flavors on the chiral transition. From calculations of Taylor expansion coefficients of the pressure w.r.t the baryon chemical potential and at imaginary chemical potentials, we discuss estimates of the QCD critical point. Those estimates make use of the universal scaling ansatz of the Lee-Yang edge singularity.