The propagation of sound in the ocean involves many complicated effects. At a basic level, the sound reflects off the ocean surface and ocean bottom, producing a sort of barber-shop mirror effect that leads to multiple images of the sound source. The strength of these echoes depends on the quality of the surface and bottom reflectors. A rough sea is more like a broken mirror that scatters sound energy; a soft silty bottom is a weak reflector that may be compared to a dark mirror. However, it gets still more complicated. The ocean sound speed depends on temperature, salinity, and depth. Gradients in these environmental parameters cause the sound to bend leading, for instance, to “convergence zone” propagation in which the sound refocuses near the ocean surface in loops spaced some 55 km apart. Modeling these effects is the province of computational ocean acoustics. This is a field that has been extensively studied over decades for navy sonar applications; however, it continues to be an active area of research. The basic physics of sound propagation in the ocean and suitable computational approaches are discussed.