The issue of tax-motivated income shifting within multinational firms has attracted increasing global attention in recent years. It is of central importance to many current policy debates, including those related to recent initiatives by the OECD on base erosion and profit shifting (BEPS) and to proposals for US tax reform in a territorial direction. This paper provides a survey of the empirical literature on tax-motivated income-shifting within multinational firms. Its emphasis is on clarifying what is known about the magnitude of BEPS. It begins by outlining a simple conceptual framework that helps to clarify aspects of governments' responses to the BEPS phenomenon and the potential role of the OECD initiative. The paper then discusses different empirical approaches to identifying income-shifting, describes existing data sources, and summarizes the findings of the empirical literature. A major theme that emerges from this survey is that in the more recent empirical literature, which uses new and richer sources of data, the estimated magnitude of BEPS is typically much smaller than that found in earlier studies. The paper seeks to provide a framework within which to conceptualize this magnitude and its implications for policy. It concludes by highlighting the importance of existing legal and economic frictions as constraints on BEPS, and discussing possible ways in which future research might model these frictions more precisely.