In acoustical oceanography, we use sound to help infer the physical characteristics of the ocean and seabed. There is a rich store of oceanographic, geological, and biological phenomena to be explored in shallow water, and we look at some of these phenomena first, with an eye toward what the current interests and challenges are. In seabed acoustics, the continental slopes and the canyons that cross-cut them are new and challenging areas to address. In physical oceanography, the full four-dimensional description of the internal wave field on the continental shelf is still a challenge. Also, the physical oceanography of the shelfbreak, continental slope, and canyons is another exciting new area. Biologically, the fact that marine life concentrates near the shelfbreak and in canyons is known, but is not well quantified. In looking at these topics, we will first address the forward propagation problem, and then decide how and if the acoustic inverse problem should be addressed. We will also discuss what specific ocean, biological, and seabed properties most need to be measured, and also how to best measure them—whether acoustically or otherwise.