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In many areas of industry, it is desirable to create geometric models of existing objects for which no such model is available. This paper reviews the process of reverse engineering of shapes. After identifying the purpose of reverse engineering and the main application areas, the most important algorithmic steps are outlined and various reconstruction strategies are presented. Pros and cons of various data acquisition techniques are described with related problems of boundary representation model construction. Specific issues addressed include characterization of geometric models and related surface representations, segmentation and surface fitting for simple and free-form shapes, multiple view combination and creating consistent and accurate B-rep models. The limitations of currently known solutions are also described, and we point out areas in which further work is required before reverse engineering of shape becomes a practical, widely-available engineering tool. This paper is intended both as an overview of current research and as an introduction to the more detailed papers of this special issue of Computer-Aided Design. It was felt that these particular papers contributed the most, amongst those submitted, to advancing the state of the art in reverse engineering.