The basic ideas of multiple testing are outlined and the problem of how to control the probability of erroneous decisions is discussed. The main emphasis is on the concept of the multiple level of significance (controlling the experiment, or family error in the strong sense) which can be achieved by applying the principle of closed tests. Various practical situations encountered in multiple testing in clinical trials are considered: more than one end point; more than two treatments, such as comparisons with a single control, comparisons using ordered alternatives, all pairwise comparisons and contrast methods; and more than one trial. Tests based on global statistics, the union intersection principle and other criteria are discussed. The application of the multiple test concept in sequential sampling is investigated. Finally some comments are made on multiple power, multiple confidence intervals and directed decisions.