Viscoplastic fluids behave like solids below a critical applied stress and flow like mobile liquids at higher stresses. They are typically composed of colloidal or nanoscale constituents, and they are prevalent in consumer products, coatings and paints, industrial fluids, foods, mineral wastes, etc. This review discusses the flow of viscoplastic fluids in systems containing several fluids separated by interfaces. Such systems include, for example, multilayer flows, films, jets, bubbles and drops and are encountered in most of applications. We review the current state of experiments, simulations and theory of viscoplastic flows in the presence of the interfaces.