There are many successful phenomenological theories that can describe the equilibrium and non-equilibrium behavior of solids at meso and macroscopic length scales. These include the Cahn-Hilliard and Allen-Cahn theories and their generalizations, commonly referred to as phase-field models. Essential ingredients to a phenomenological theory are materials specific thermodynamic potentials and kinetic coefficients. These quantities are often difficult if not impossible to measure in isolation. An alternative approach is to rely on first-principles statistical mechanics methods to calculate free energies, kinetic transport coefficients and chemo-mechanical constitutive relations. In this talk, I will describe recent advances in first-principles statistical mechanics methods of multicomponent crystals and illustrate how they can be applied to important metallurgical problems, including precipitation in Mg alloys, phase stability in high-entropy refractory alloys, diffusion and order-disorder phenomena in superalloys and oxidation processes of titanium alloys. Recent applications of machine learning in scale bridging will also be reviewed.