Controlling interfaces of phase separating fluid mixtures is key to creating diverse functional soft materials. Traditionally, this is accomplished with surface-modifying agents. Using a combination of experiment and theory, we study how mechanical activity shapes soft interfaces of a phase separating mixture of an active and a passive fluid. Chaotic flows in the active fluid give rise to giant interfacial fluctuations and non-inertial propagating active waves. At high activities, stresses disrupt interface continuity and drive droplet pinch- off. In this limit, we observe an active emulsion-like steady-state comprising finite-sized droplets that constantly break apart, fuse and exchange content. Furthermore, when in contact with a solid boundary, active interfaces exhibit non-equilibrium wetting transitions, where the fluid powered by active stress climbs the wall against gravity. These results demonstrate the promise of me- chanically driven interfaces for creating a new class of lifelike soft active mat- ter.