The decade of the 1950s marks the beginning of acoustic signal processing as a subfield of underwater acoustics. The forerunner, signal recognition, gradually evolved into a unified class of spatial and temporal processing techniques and theory which came to stand on its own. The doctrines that emerged in that decade, such as spectrum analysis, correlation, and multiple beamforming, have continued to grow in sophistication, until we now find methods such as the fast Fourier transform, sequential detection, and adaptive beamforming handed down to us from the 1960s. The milestones of signal processing over the past 20 years present a striking record of progress in that field.