This chapter surveys the boundedly rational heterogeneous agent (BRHA) models of financial markets, to the development of which the authors and several co-authors have contributed in various papers. We give particular emphasis to role of the market clearing mechanism used, the utility function of the investors, the interaction of price and wealth dynamics, portfolio implications, the impact of stochastic elements on the markets dynamics, and calibration of this class of models. Due to agents? behavioural features and market noise, the BRHA models are both nonlinear and stochastic. We show that the BRHA models produce both a locally stable fundamental equilibrium corresponding to that of standard paradigm, as well as instability with a consequent rich range of possible complex behaviours characterised both indirectly by simulation and directly by stochastic bifurcations. A calibrated model is able to reproduce quite well the stylized facts of financial markets. The BRHA framework is thus able to accommodate market features that seem not easily reconcilable for the standard financial market paradigm, such as fat tail, volatility clustering, large excursions from the fundamental and bubbles.