The results of theoretical and experimental investigations of conversion of infrared radiation to the visible (or ultraviolet and near infrared) range are summarized. An analysis is made of the physical basis of the process, which involves generation of the sum or difference frequency in media with a quadratic nonlinear polarizability. In particular, the critical and noncritical phase matching, the angular and spectral widths of the phase-matching curve, the energy and quantum efficiency of the conversion process, and similar topics are considered. The applications of the conversion process in detection of infrared signals, infrared vision, and nonlinear infrared spectroscopy are dealt with. Typical results obtained so far are given briefly. The following topics are discussed: the criteria for selection of nonlinear media useful for the near and middle infrared range; detection of thermal infrared signals; response time and other parameters of nonlinear media; methods for the calculation of the spatial (angular) structure of the output radiation and its relationship to the structure of the initial infrared field; spatial resolution and number of resolved elements in parametric infrared viewers; comparison of systems based on tangential (noncritical) and critical vector phase matching; and so on. Spectral resolution and response time of nonlinear infrared spectroscopic methods are discussed. It is shown that various parametric detector analyzers for the infrared range are in many respects not inferior or considerably better than conventional infrared devices. This applies particularly to the response time because parametric converters have no competitors in, for example, picosecond infrared spectroscopy. Extensive use of parametric infrared converters in science and technology will represent a new stage in the mastering of the infrared range.