This paper describes a geometric approach to underwater 3-D scene reconstruction using sonar range sensing. Our goal is to recover explicit geometric surface descriptions for man-made objects, by focusing the geometric constraints of multiple sonar returns obtained from different sensing locations by a moving autonomous underwater vehicle (AUV). We employ a simplified physical model of the sonar sensing process, based on the geometrical acoustics high-frequency approximation of acoustic scattering. Our current research effort is directed to support the task of locating and retrieving rigid objects from the deep ocean seafloor, using an untethered AUV. The key open problems concern the development of (1) robust methods for 3-D shape recovery, (2) an effective data association procedure, and (3) directed sensing strategies to control the data acquisition process.