Financial markets have undergone a remarkable transformation over the past two decades due to advances in technology. These advances include faster and cheaper computers, greater connectivity among market participants, and perhaps most important of all, more sophisticated trading algorithms. The benefits of such financial technology are evident: lower transactions costs, faster executions, and greater volume of trades. However, like any technology, trading technology has unintended consequences. In this paper, we review key innovations in trading technology starting with portfolio optimization in the 1950s and ending with high-frequency trading in the late 2000s, as well as opportunities, challenges, and economic incentives that accompanied these developments. We also discuss potential threats to financial stability created or facilitated by algorithmic trading and propose “Financial Regulation 2.0,” a set of design principles for bringing the current financial regulatory framework into the Digital Age.