There are many situations where active fluids coexist with passive ones. In bacterial swarms, internal boundaries separate cells of different type or live and dead cells. In cell biology the evidence for the formation of membraneless organelles has fueled interest in the role of active processes in liquid-liquid phase separation. Inspired by recent experiments that combine a microtubule-based active liquid crystalline fluid with an immiscible binary polymer mixture, we have used numerical and analytical methods to explore how active stresses and associated active flows modify the properties of the soft interfaces in a phase separating mixture. In this talk I will describe some of the intriguing phenomena revealed by theory and experiments, such as giant interfacial fluctuation, traveling interfacial waves, activity suppressed phase separation, and activity controlled wetting transitions.