Twenty-one years after its appearance, Cox's 1972 paper on Regression models and life tables continues to be one of the most frequently cited publications in the scientific and medical literature. The proportional-hazards model and partial-likelihood technique have been applied to thousands of data sets, not always appropriately, and have motivated hundreds of theoretical studies, not always relevant. Recent developments are reviewed and continuing problems discussed, especially with respect to predictive inference. The accuracy of model-based predictions, and how they compare with consultants' judgements are investigated by means of an example.