This working paper gives an overview of the current debate on monetary policy reactions to asset prices, focusing on the developments on equity markets in the United States. It first describes the main causes and consequences of these developments and then surveys the pros and cons of a monetary policy reaction. The standard approach relying on the Gordon-Shapiro equation fails to justify the current high price levels on US stock markets. Several limits to Gordon-Shapiro's perfect competition model are proposed in order to explain the gap between observed and "justified" data. Equity prices affect investment and consumption through several channels. Although monetary policy should not ignore asset price fluctuations, it is fairly generally thought that it should take them into account only in so far as they affect inflation.