We survey the academic literature that examines the risks and returns of private equity investments, optimal private equity allocation, and compensation contracts for private equity firms. The irregular nature and limited data of private equity investments complicate the estimation and interpretation of standard risk and return measures. These complications have led to substantial disparity in performance estimates reported across studies. Moreover, studies suggest that the illiquidity and transaction costs inherent in private equity investments have substantial implications for optimal holdings of these assets. While incentive fees in private equity address moral hazard and information agency problems, total fees in private equity investments are very large and incentive fees account for a minority of total compensation.