Computer-aided tomography (CAT) is a method of laminar reconstruction of the structure of an inhomogeneous and generally asymmetric three-dimensional object from a set of measured projections. Recently CAT has been widely used, not only in medical diagnostics, where most brilliant and impressive results have been achieved, but also in various areas in physics. Physical and technical applications of CAT are the topic of the present review. The basic principles of tomography research are described, CAT problems are classified from the point of view of integral geometry, and the main algorithms used in computational data processing are briefly commented upon. Particular attention is devoted to possible CAT applications to defectoscopy, microscopy, solid state physics, geophysics, Earth and planetary atmospheric physics, aeroand hydrodynamics, and plasma physics. The main developmental directions of theoretical and technical CAT in the near future are noted in conclusion.