Some aquatic animals, most notably cetaceans, have evolved sophisticated echo-detection systems over millions of years for locating and identifying underwater targets such as their fish and squid prey. Perhaps inspired by nature, the first man-made echo-detection instruments (echosounders) were developed in the early 1900s, primarily for submarine detection and to measure water depth. Echosounders were used in commercial marine fisheries in the 1930s and 40s to detect fish, and fisheries scientists quickly realised the potential of echosounding for monitoring important fish stocks. The field of scientific fisheries acoustics was born in the late 1960s, and by the end of the 1980s echosounders had become widely trusted as a tool capable of delivering robust quantitative fish-stock estimates. In marine and freshwater environments around the world, echosounding is one of the primary fish-stock assessment tools employed by many state and federal government agencies, research organisations and private companies. We present a number of case studies to illustrate the range of approaches currently employed and the strengths and limitations of quantitative echosounding.