The importance of configurational, vibrational, and electronic excitations in crystalline solids of technological interest makes a rigorous treatment of thermal excitations an essential ingredient in first-principles models of materials behavior. This contribution reviews statistical mechanics approaches that connect a crystal's electronic structure to its thermodynamic and kinetic properties. We start with a description of a thermodynamic and kinetic framework for multicomponent crystals that integrates chemistry and mechanics, as well as nonconserved order parameters that track the degree of chemical order and group/subgroup structural distortions. The framework allows for spatial heterogeneities and naturally couples thermodynamics with kinetics. We next survey statistical mechanics approaches that rely on effective Hamiltonians to treat configurational, vibrational, and electronic degrees of freedom within multicomponent crystals. These Hamiltonians, when suitably constructed, are capable of extrapolating first-principles electronic structure calculations within (kinetic) Monte Carlo simulations, thereby enabling first-principles predictions of equilibrium and nonequilibrium materials properties at finite temperature.