The paper reviews the methods developed for predicting the reliability of systems, based upon design information, failure data on components, extrapolation from test data, and the use of mathematical models which relate predicted reliability to the various factors which can affect it, such as stress, application environments, quality and reliability programme activities. The fundamental limitations inherent in reliability prediction and modelling, related to logical, physical and human factors aspects, are described. The paper concludes with approaches that should be adopted to ensure that reliability predictions are realistic and credible, taking full account of physical and managerial factors involved in design, development and production.