Separation processes are major contributors to production cost and energy usage in the chemical, petrochemical, and pharmaceutical industries, and phase and sorption equilibria play a major role in biological, environmental, and geological systems. Thus, predictive modeling of phase and sorption equilibria is pivotal for improving separation processes and for understanding complex chemical systems. This presentation will highlight progress in two distinct areas: (i) first principles Monte Carlo simulations (with the interactions described by Kohn-Sham density functional theory) aimed at predicting the unary vapor-liquid equilibria for water, methanol, and methane and the Gibbs free energy of solvation/dissociation for hydrogen chloride; and (ii) large-scale Gibbs ensemble Monte Carlo simulations (with the interactions described by molecular mechanics force fields) to explore liquid-liquid extraction and zeolite-based sorption processes for the separation of ethanol and other oxygenates from aqueous solution.