This paper reviews the empirical literature on heterogeneous beliefs and asset price dynamics that challenges the traditional rational agent framework. Emphasis is given to the validation and estimation of (dynamic) heterogeneous agent models that have their roots in the agent-based literature. Heterogeneous agent models perform well in describing, explaining, and often forecasting asset markets dynamics, such as equities, foreign exchange, credit, housing, derivatives, and commodities. Our survey suggests that heterogeneous agent models have the ability to produce important stylised facts observed in financial time series and to replicate important episodes of financial turmoil.