Phase separation of liquids, as illustrated by everyday oiland water mixtures, provides the basis for creating diverse soft materials, fromlipid vesicles to emulsions. These states of matter are typically formed uponthe addition of surface adsorbing agents that stabilize liquid interfaces. Iwill show that active matter provides a new way for controlling phaseseparation. Active fluids contain microscopic energy consuming objects thatdrive far-from-equilibrium large-scale flows. When combined with liquid-liquidphase separation, active matter completely partitioned to one of the phases. Bulkflowsin the active phase produced waves along phase boundaries whose amplitude is setby activity. These dynamic modes lead to a finite-size steady state, wherecoalescence of smaller droplets is balanced by the break-up of larger ones. Wheninterfaces meet a solid boundary, active waves also drive non-equilibriumwetting transitions. These results demonstrate the promise ofmechanically-driven interfaces for creating a new class of soft active matter.