It is argued that the provision of accurate and useful probabilistic assessments of future events should be a fundamental task for biostatisticians collaborating in clinical or experimental medicine, and we explore two aspects of obtaining and evaluating such predictions. When covariate information on patients is available, logistic regression and other multivariate techniques are often used to select prognostic factors and create predictive models. An example shows how the explicit aim of prediction needs to be taken into account in such modelling, and how predictive performance may be assessed by decomposition of a scoring rule. Secondly, results from a program that provides pretrial and interim predictions in clinical trials are displayed, bringing together the use of subjective opinion, Bayesian methodology and techniques for evaluating and criticizing predictions.