This is the fifth paper in a series of reviews presented at 8-year intervals starting in 1979 [J. Acoust. Soc. Am. 65, S42 (1979); 82, S102 (1987); 97, 3312 (1995); 114, 2430 (2003)]. All surveys cover basic acoustic models and sonar-performance models. Basic acoustic models include propagation, noise, and reverberation models. Propagation models are categorized according to ray theory, multipath expansion, normal mode, fast field, and parabolic approximation formulations; further distinctions are made between range-independent and range-dependent solutions. Noise models include ambient noise and beam-noise statistics models. Reverberation models include cell and point-scattering formulations. Sonar-performance models include active sonar models, model operating systems, and tactical decision aids. Active sonar models integrate basic acoustic models, signal processing models, and supporting databases into cohesive operating systems organized to solve the sonar equations. Model-operating systems provide a framework for the direct linkage of data-management software with computer-implemented codes of acoustic models. Tactical decision aids represent a form of engagement-level simulation that blend environmental and sonar-performance information with tactical rules. The current inventory of underwater acoustic models comprises 128 propagation models, 21 noise models, 28 reverberation models, and 35 sonar-performance models. Since 1979, approximately five models have been added to the inventory each year.