The purpose of this paper is to develop, from basic considerations, a complete set of equations governing the evolution of a sharp interface separating two fluid phases undergoing transformation. For situations in which a phase transformation does not occur, so that the phase interface is a material surface, the governing bulk and interfacial equations are well-developed and agreed upon. Focusing on the interface, the relevant equations are the conventional balances for mass, linear momentum, and energy, augmented by suitable constitutive equations. But when a phase transformation does occur, the interfacial expressions for balance of mass, momentum, and energy fail to provide a closed description and must be supplemented by an equation that accounts for the microphysics underlying the exchange of material between phases. For this purpose we employ the formalism of configurational forces to derive the appropriate generalization of the Gibbs-Thomson equation for a fluid-fluid interface under non-equilibrium conditions.