Multilevel data are structures that consist of multiple units of analysis, one nested within the other. Such data are becoming quite common in political science and provide numerous opportunities for theory testing and development. Unfortunately, this type of data typically generates a number of statistical problems, of which clustering is particularly important. To exploit the opportunities offered by multilevel data, and to solve the statistical problems inherent in them, special statistical techniques are required. In this article, we focus on a technique that has become popular in educational statistics and sociology-multilevel analysis. In multilevel analysis, researchers build models that capture the layered structure of multilevel data, and determine how layers interact and impact a dependent variable of interest. Our objective in this article is to introduce the logic and statistical theory behind multilevel models, to illustrate how such models can be applied fruitfully in political science, and to call attention to some of the pitfalls in multilevel analysis.