Fostered by a growing interest in nonlinear control theory and catalyzed by the discovery in the early 1980s of the exact conditions under which a nonlinear plant can be linearized by static-state feedback and coordinate transformation, in the last decades there has been a rapid increase of interest in the search for approximate solutions to the problem of linearizing nonlinear systems by state or output feedback. Main reason for that is the limited applicability of the rigorous methods, and the complexity, sensitivity and design di$culties of the exact linearizing compensators, if any. In the present paper, the literature on the subject is reviewed and organized in what is believed to be a new and consistent perspective. Recent works, especially in the area of data-based techniques, are in fact described and related, whenever possible, to fundamental results previously obtained by model-based di!erential geometric methods; this is expected to bring modern system linearization methods closer to the needs of practicing control engineers and to stimulate further research eventually able to "ll visible gaps in this direction.