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. •Surficial mass movements are common in volcanic areas and generate signals that are recorded by seismic and acoustic arrays.•Our understanding of the relation of these signals to characteristics of the mass movement is limited but improving.•We review the literature on the study of mass movements at volcanoes using seismic and acoustic monitoring.•We discuss future research directions and steps toward operational monitoring.