Controlling interfacial structure and dynamics of phase separating fluid mixtures is key to creating diverse functional materials. Traditionally, this is accomplished by controlling interface chemistry, through the presence of surface-modifying amphiphilic agents. Using a phase separating mixture of active and passive fluids, we study how mechanical activity controls soft interfaces. Feedback between the stresses generated in the fluid’s bulk and low interfacial tension give rise to giant interfacial fluctuations and non-inertial traveling waves that propagate along the phase boundary. Active interfaces arrest the phase separation dynamics, creating finite-size droplet distribution maintained by the balance of the enhanced coalescence of smaller motile droplets and the spontaneous break-up of larger ones. When in contact with a solid wall, active interfaces also exhibit non-equilibrium wetting transitions, where the fluid climbs the wall against gravity. These results demonstrate the promise of mechanically-driven interfaces for creating a new class of soft active matter.