This paper presents the phenomenology of different approaches to the frequency-shifting (upconversion) of infrared radiation into the visible and discusses the practical aspects of designing systems to upconvert IR images. The recently discovered process of upconverting infrared radiation into the visible or the ultraviolet using two-photon-pumped alkalimetal vapors and the more familiar method of frequency mixing using single-photon-pumped nonlinear crystals are described and compared. In addition to these coherent processes, the use of quantum-counter action in certain crystals to convert an IR photon into a visible photon by an incoherent process is discussed. The important performance parameters of an IR imaging system are discussed briefly and the considerations and constraints involved in the design of coherent and incoherent image upconverter systems are presented. Using this background, practical system designs are developed for both active and passive imaging. The expected performances of these systems are compared with those of IR imaging systems based on direct-detection of IR photons with semiconductor detectors.