The impact of money on politics—whether through campaign finance, lobbying, or independent expenditure—raises key normative questions about democratic representation and accountability. In recent years there has been a deluge of new data allowing researchers to study money in politics from new and exciting perspectives. As a complement to this trend, there has also been a resurgence of interest in developing formal models to provide new theoretical insights that can help us understand how, why, and when money influences politics and policy. We review several major themes in this literature, focusing specifically on exchange-based models, informational models, and subsidy-based models. We compare and contrast the key contributions, and limitations, of each approach in understanding the role of lobbying and campaign finance in politics. We also discuss future avenues for research that incorporate aspects of each approach, which, we believe, will introduce new theoretical insights for understanding special interest influence.