Classical pluralists, the authors of The Federalist Papers, and many modern scholars have emphasized the critical role of the interests in shaping policies. Still, in general, deductive theory has not provided the hypotheses and explanations offered by political science in studying interests. Economists studying interest groups have taken a more abstract, analytical approach, but this work is largely unknown in political science, perhaps because it is enshrouded in jargon and arcane terminology. We review this literature, using as our motivation two fundamental questions: First, how do interest groups influence policy in a democracy? Second, how should the institutions of government be designed to encourage or control this influence? The models we review are generally of a formal, mathematical nature, but we focus solely on their intuitive content and their contribution to our knowledge of democracy and representation.