The presence of interfaces can have a dramatic effect on phase behavior in materials.  In this talk, I first describe a thermodynamic analysis of interfacial layering (complexion) transitions at grain boundaries in binary alloys using both simplified lattice models and off-lattice semi-grand-canonical Monte Carlo simulations.  In particular, complexion diagrams are developed for these alloys that highlight the richness of the phase-like behavior of the system and, in particular, a series of first-order transitions and associated critical points.  I will also describe the impact of these transitions on grain-boundary kinetics (i.e., boundary mobility) and the Kapitza resistance of grain boundaries using atomistic simulation, and then discuss the possibility of phonon engineering.