In this perspective article, we introduce elasto-plastocapillarity: surface-tension-driven free-surface flows of yield-stress fluids in which capillary stresses compete with yielding and elastic relaxation. We frame the relevant parameter space, and highlight representative problems (drops, bubbles, jets/filaments, thin films, and porous media) that are central to applications ranging from additive manufacturing and coatings to biological flows. We then outline a set of timely open challenges, including surface-tension measurements, breakdown of scale separation near the microstructures, coupled bulk-interface flow experimental diagnosis, interfacial rheology and surface stresses, history dependence, constitutive models and boundary conditions, reduced theoretical models, and the emerging opportunity provided by artificial intelligence and microgravity; aimed at guiding future experiments, theory, and computation.