Bayesian statistical methods are being used increasingly in clinical research because the Bayesian approach is ideally suited to adapting to information that accrues during a trial, potentially allowing for smaller more informative trials and for patients to receive better treatment. Accumulating results can be assessed at any time, including continually, with the possibility of modifying the design of the trial, for example, by slowing (or stopping) or expanding accrual, imbalancing randomization to favour better-performing therapies, dropping or adding treatment arms, and changing the trial population to focus on patient subsets that are responding better to the experimental therapies. Bayesian analyses use available patient-outcome information, including biomarkers that accumulating data indicate might be related to clinical outcome. They also allow for the use of historical information and for synthesizing results of relevant trials. Here, I explain the rationale underlying Bayesian clinical trials, and discuss the potential of such trials to improve the effectiveness of drug development.