The interaction of neutrons over a wide energy range with matter can be applied in computerized tomography (CT) to obtain nondestructive insight into objects, which is highly complementary to the information obtained by the classical method of X-ray tomography. Systematic tomography studies with thermal neutrons, fast neutrons of different spectral composition, and mixed neutron and gamma fields have been done in recent years. The experiments were performed at the Munich research reactor [Forschungsreaktor München (FRM)] of the Technical University of Munich. Examples of CT measurements demonstrate the manifold possibilities of the interdisciplinary cooperation of neutron physics and materials research.The necessary equipment and some specific problems in the processing of measured transmission rates for image reconstruction are described.