Each episode of volatility in financial markets heightens the attention of government officials and others to the role played by the hedge fund industry in financial market dynamics. Hedge funds were implicated in the 1992 crises that led to major exchange rate realignments in the European Monetary System, and again in 1994 after a period of turbulence in international bond markets. Concerns mounted in 1997 in the wake of the financial upheavals in Asia. And they were amplified in 1998, with allegations of large hedge fund transactions in various Asian currency markets and with the near collapse of a major hedge fund, Long-Term Capital Management (LTCM). This paper discusses the size, number, and investment styles of hedge funds, and their interactions with global financial markets. It reviews the present state of their supervision and regulation, and assesses various suggestions for regulating them more closely, often as part of new regulatory approaches to the larger financial markets of which hedge funds are but a small part.