Technological advances and regulatory initiatives have led to the emergence of a competitive, but fragmented, equity trading landscape in several markets around the world. While these changes have coincided with benefits like reduced transaction costs, advancements in trading technology, and access to a diverse array of execution venues, regulators and market participants have also raised concerns about the welfare implications of innovations like dark pools as well as the resulting increase in execution complexity. Exchanges are often viewed as natural monopolies due to the presence of network externalities and economies of scale. However, heterogeneity in traders' preferences means that no single venue can serve the interests of all investors. Fragmentation of the marketplace can be seen as a direct outcome of this heterogeneity. In this paper, we review the theoretical and empirical literature examining the economic arguments and motivations underlying market fragmentation, the resulting implications for liquidity and price efficiency, and the role for public policy. Beyond the concerns for equity markets, the lessons from this literature are relevant for other asset classes experiencing an increase in competition between trading venues.