Chapter 7. Agent Based Models for Market Impact and Volatility Financial markets display a host of universal “stylized facts” begging for a scientific explanation: Excess volatility fat tails and clustered activity are well known and have been studied for many years. More microstructural stylized facts have recently emerged for example the long memory of the order flow or the square root dependence of impact on the volume of metaorders. Agent based models are attempts to account for these stylized facts in a unified manner. Devising faithful microstructural ABMs would allow one to answer crucial questions such as those related to market stability. Can large orders destabilize markets Is HFT activity detrimental Can destabilizing feedback loops be mitigated by adequate regulation The present review paper summarizes recent work in that direction. We discuss in particular the Santa Fe zero intelligence model which provides a very interesting benchmark but suffers from important drawbacks as well such as strong mean reversion effects. One can enrich the Santa Fe model as to reproduce both diffusive prices and the square root impact law. The underlying mechanism can be well understood in terms of a generic “reaction–diffusion” model for the dynamics of the liquidity which can be solved analytically. Finally we argue that the role of “information” is probably overstated in classical theories while a picture based on a self reflexive price impacting order flow has many merits. The recent accumulation of microstructural stylized facts allowing one to focus on the price formation mechanism all but confirm that fundamental information plays a relatively minor role in the dynamics of financial markets at least on short to medium time scales.