This document is the result of a survey of published geometric dimensioning and tolerancing theories and post-inspection data-analysis algorithms. Both traditional and modern theories have been reviewed. Principles on which current national standards and international standards are based have been stated. These geometric dimensioning and tolerancing principles are commonly used in mechanical design and part inspection. Post-inspection data- analysis algorithms, used for extracting features and evaluating tolerances, have also been reviewed. The effects of using different fitting criteria are discussed. From this theory and algorithm review, we recommend directions for future development in these areas. The bibliography covers activities and accomplishments of the research in advancing inspection technology.