Decisions to terminate clinical trials have been the subject of intense debate, both before and after the actual decisions are made. This situation reflects the unique character of studies involving human subjects in that the decision to stop is largely an ethical one in which the statistical considerations play a major, but not a dominating, role. This can be constrasted with, say, that of acceptance sampling in which statistical qua economic considerations completely determine the stopping rule. It is important for all investigators involved in clinical studies to be aware of the sequential nature of the analyses of those studies. In particular, they must be conscious of the inappropriateness of the usual "P values" when repeated analyses of accumulating data are done. There is a pressing need to develop more realistic statistical theory and methodology, as well as to apply existing techniques, where appropriate, particularly in view of the numerous practical and theoretic difficulties that hinder application of sequential techniques in clinical trials. This paper gives some historical background on sequential trials, describes the different classes of trials, and lists some important reasons why sequential trials are not used more often.