Stock market anomalies representing the predictability of cross-sectional stock returns are one of most controversial topics in financial economic research. This chapter reviews several well-documented and pervasive anomalies in the literature, including investment-related anomalies, value anomalies, momentum and long-term reversal, size, and accruals. Although anomalies are widely accepted, much disagreement exists on the underlying reasons for their predictability. This chapter surveys two competing theories that attempt to explain the presence of stock market anomalies: rational and behavioral. The rational explanation focuses on the improvement of the existing asset pricing models and/or searching for additional risk factors to explain the existence of anomalies. By contrast, the behavioral explanation attributes the predictability to human behavioral biases in collecting and processing financial information, as well as in making investment decisions.