We survey the literature documenting the rise of sovereign wealth funds (SWFs), which, with assets under management of over $5.4 trillion at year‐end 2014, are a major force in global finance. Research papers have analyzed the evolution of SWFs from stabilization funds to stand‐alone wealth management funds; we both survey this research and show that more than 25 countries have launched or proposed new SWFs since January 2008. The most salient and controversial feature of SWFs is that they are state‐owned; we survey the existing literature on state ownership and discuss what this predicts about the efficiency and beneficence of government control of SWF assets. We discuss the documented importance of SWF funding sources (oil sales revenues versus excess reserves from export earnings) and survey the normative literature describing how SWFs should allocate funds. We then summarize the empirical literature studying how SWFs actually do allocate funds—across asset classes, geographically, and across industries. We document that most SWF equity investments in publicly traded firms involve cross‐border purchases of sizeable minority stakes (median around 20%) in target firms, with a strong preference for investments in the financial sector. Next, we assess empirical studies examining the impact of SWF stock investments on target firm financial and operating performance, and find universal support for a positive announcement period stock price increase of 1–3%. This, however, is significantly lower than the 5% abnormal return documented for stock purchases by comparable privately owned financial investors in recent studies, indicating a “sovereign wealth fund discount.” We conclude by summarizing the lessons of SWF research and pointing out unresolved issues.