The authors examine current areas of concern in the regulation of secondary trading markets. The topics include questions concerning the operation of Regulation NMS, transparency and dark liquidity, algorithmic and high-frequency trading, the duties and obligations of broker-dealers who handle customer orders, system robustness, and market data issues. The authors also discuss several topics related to fixed income markets. For each topic, the authors examine the academic literature as well as practical regulatory considerations. Where possible, the authors draw conclusions from the previous literature and offer suggestions for future rulemaking.