This chapter begins with a discussion of the comparative difficulty of measuring horizontally integrated subsurface oceanic current and vorticity measurements. This is followed by a discussion of computer-assisted tomography techniques used in the medical, geophysical, and seismic branches of science and their adaptation and extension to acoustic tomography for subsurface oceanographic investigations. In particular, the following aspects pertaining to the application of acoustic methods for probing the oceans’ interior water temperature and current structure, as well as their adaptations for measuring horizontally averaged water currents from straits, coastal water bodies, estuaries, and rivers, are addressed: (1) one-way tomography, (2) two-way tomography (reciprocal tomography), (3) acoustic tomographic measurements from straits, (4) coastal acoustic tomography (CAT), (5) river acoustic tomography (RAT), (6) acoustic tomographic measurements of vorticity, and (7) horizontally integrated current measurements using space-time acoustic scintillation analysis technique.