Monitoring interim accumulating data in a clinical trial for evidence of therapeutic benefit or toxicity is a frequent policy, usually carried out by an independent scientific committee. Repeated testing at conventional critical values can substantially inflate the type I error rate. To maintain acceptable levels, group sequential and stochastic curtailment have been developed for clinical trials. One should not view such methods as absolute rules, but as useful guides. The decision process to terminate a trial early is complex and necessitates an accounting for many factors. The Beta-Blocker Heart Attack Trial provides an excellent example of many of these issues.