In this chapter we discuss the problem of identifying differentially expressed genes from a set of microarray experiments. Statistically speaking, this task falls under the heading of 'multiple hypothesis testing.' In other words, we must perform hypothesis tests on all genes simultaneously to determine whether each one is differentially expressed. Recall that in statistical hypothesis testing, we test a null hypothesis vs an alternative hypothesis. In this example, the null hypothesis is that there is no change in expression levels between experimental conditions. The alternative hypothesis is that there is some change. We reject the null hypothesis if there is enough evidence in favor of the alternative. This amounts to rejecting the null hypothesis if its corresponding statistic falls into some predetermined rejection region. Hypothesis testing is also concerned with measuring the probability of rejecting the null hypothesis when it is really true (called a false positive), and the probability of rejecting the null hypothesis when the alternative hypothesis is really true (called power).