Changes in the ocean soundscape have been driven by anthropogenic activity (e.g., naval-sonar systems, seismic-exploration activity, maritime shipping and windfarm development) and by natural factors (e.g., climate change and ocean acidification). New regulatory initiatives have placed additional restrictions on uses of sound in the ocean: mitigation of marine-mammal endangerment is now an integral consideration in acoustic-system design and operation. Modeling tools traditionally used in underwater acoustics have undergone a necessary transformation to respond to the rapidly changing requirements imposed by this new soundscape. Advanced modeling techniques now include forward and inverse applications, integrated-modeling approaches, nonintrusive measurements, and novel processing methods. A 32-year baseline inventory of modeling techniques has been updated to reflect these new developments including the basic mathematics and references to the key literature. Charts have been provided to guide soundscape practitioners to the most efficient modeling techniques for any given application.