We use theory and computer simulation to study molecular phenomena at the frontiers of physical chemistry. The systems we study are diverse – ranging from aqueous solutions and interfaces, to biomolecular assemblies, to nanoscale materials – yet they share essential motifs of disorder and heterogeneity. Using the tools of modern statistical mechanics, we explore the emergent physical principles which govern these complex molecular systems. Our current interests are linked by several physical themes. Fluctuating interfaces, for example, figure prominently in studies of ion solvation near the air-water interface, as well as studies of phase coexistence within nanostructures and photosynthetic membranes. As another example, processes of self-assembly in chemical, biological, and materials contexts generically pit kinetics against thermodynamics in ways that demand broad new capabilities of theory and simulation. Our work is strongly shaped by collaboration with experimental laboratories.