The aim of this review is to acquaint the reader with the principles and methods of ion radiography—a method of studying the inner structure of an object by using heavy charged particles. Along with the refinement of the traditional x-ray method of diagnostics and the development of a number of new methods, such as positron tomography and nuclear magnetic resonance, and in spite of the great advances attained in xradiography in recent years, a persistent search continues for new, refined methods. First of all, efforts are directed toward seeking effective methods of early diagnosis of tumor lesions with less danger than in xradiography. Studies have been conducted in a number of countries in the past decade on the possibility of applying heavy charged particles of relatively high energies for these purposes. Ion radiography enables one to obtain a higher contrast image than x-radiography at lower doses of irradiation, and to differentiate soft tissues and to detect in them anomalies of small dimensions. It opens up the possibility of obtaining new diagnostic information. Theoretical studies in the field of ion radiography and experiments on animals, on human tissues, and in a number of cases, on patients, have shown the promise offered by using ions for diagnosing not only tumors, but also a number of other serious lesions. This new field of study has incorporated the experience of particle and nuclear physics and widely employs its variety of investigational methods. This article also treats problems involving the application of accelerators for ion radiography and specifications for the beam parameters and for the particle detectors. This review gives an account of the advances in this new field of studies and the prospects for its development and the difficulties on the pathway of introducing it into practice.