We discuss recent progress in constraining the QCD phase diagram at finite baryon density. The entropy contour construction based on lattice QCD input suggests a candidate critical region near T ~ 110 MeV and muB ~ 600 MeV, conditional on the low-order extrapolation. The analysis is extended to physical directions in the four-dimensional space of chemical potentials, including strangeness neutrality (heavy-ion collisions), beta equilibrium (neutron stars), and isospin asymmetry (early Universe). We also present a Bayesian inference of baryon number susceptibilities from RHIC-BES-II proton cumulant data based on maximum entropy freeze-out and exact baryon conservation.