Many scientific experiments subject to rigorous statistical analyses involve the simultaneous evaluation of more than one question. For example, in clinical trials one may compare more than one treatment group with a control group, assess several outcome variables, measure at various time points, analyze multiple subgroups or look at any combination of these and related questions; but multiplicity problems occur if we want to make simultaneous inference across multiple questions. Similar problems may arise in agricultural field experiments which simultaneously compare several irrigation systems, investigate the dose response relationship of a fertilizer, involve repeated assessments of growth curves for a particular culture, etc. Recently, high-dimensional screening studies have become widely available in molecular biology and its applications, such as gene expression experiments and high throughput screenings in early drug discovery. Those screening studies have in common the problem of identifying a small subset of relevant variables from a huge set of candidate variables (e.g., genes, compounds, proteins). Scientific research provides many examples of well-designed experiments involving multiple investigational questions. Multiplicity is likely to become important when strong evidence and good decision making is required.