This tutorial discusses important statistical problems arising in clinical trials with multiple clinical objectives based on different clinical variables, evaluation of several doses or regiments of a new treatment, analysis of multiple patient subgroups, etc. Simultaneous assessment of several objectives in a single trial gives rise to multiplicity. If unaddressed, problems of multiplicity can undermine integrity of statistical inferences. The tutorial reviews key concepts in multiple hypothesis testing and introduces main classes of methods for addressing multiplicity in a clinical trial setting. General guidelines for the development of relevant and efficient multiple testing procedures are presented on the basis of application-specific clinical and statistical information. Case studies with common multiplicity problems are used to motivate and illustrate the statistical methods presented in the tutorial, and software implementation of the multiplicity adjustment methods is discussed. Copyright © 2013 John Wiley & Sons, Ltd.