Over the 50 years of its existence, Baarda’s concept of reliability has been used as a standard practice for the quality control in geodesy and surveying. In this study, we analysed the pioneering work of Baarda (Publ Geod New Ser 2(4) 1967; Publ Geod New Ser 2(5) 1968) and recent studies on the subject. We highlighted that the advent of personal computers with powerful processors has rendered Monte Carlo method as an attractive and cost-effective approach for quality control purposes. We also provided an overview of the latest advances in the reliability theory for geodesy, with particular emphasis on Monte Carlo method.