Surficial mass movements, such as debris avalanches, rock falls, lahars, pyroclastic flows, and outburst floods, are a dominant hazard at many volcanoes worldwide. Understanding these processes, cataloging their spatio-temporal occurrence, and detecting, tracking, and characterizing these events would advance the science of volcano monitoring and help mitigate hazards. Seismic and acoustic methods show promise for achieving these objectives: many surficial mass movements generate observable seismic and acoustic signals, and many volcanoes are already monitored. Significant progress has been made toward understanding, modeling, and extracting quantitative information from seismic and infrasonic signals generated by surficial mass movements. However, much work remains. In this paper, we review the state of the art of the topic, covering a range of scales and event types from individual rock falls to sector collapses. We consider a full variety of volcanic settings, from submarine to subaerial, shield volcano to stratovolcano. Finally, we discuss future directions toward operational seismo-acoustic monitoring of surficial mass movements at volcanoes.