We survey recent developments in finance that analyze how heterogeneous beliefs among investors generate speculation and trading. We describe the joint effects of heterogeneous beliefs and short-sales constraints on asset prices, using both static and dynamic models, discuss the no-trade theorem in the rational expectations framework, and present investor overconfidence as a potential source of heterogeneous beliefs. We review recent results of Scheinkman and Xiong (2003) modeling the resale option that is embedded in share prices in the presence of short-sale constraints and heterogeneous beliefs, highlighting the implied correlation between stock prices and trading volume. Finally, we discuss the survival of investors with incorrect beliefs.