One approach to the analysis of stochastic fluctuations in market prices is to model characteristics of investor behaviour and the complex interactions between market participants, with the aim of extracting consequences in the aggregate. This agent-based viewpoint in finance goes back at least to the work of Garman (1976) and shares the philosophy of statistical mechanics in the physical sciences. We discuss recent developments in market microstructure models. They are capable, often through numerical simulations, to explain many stylized facts like the emergence of herding behavior, volatility clustering and fat tailed returns distributions. They are typically queueing-type models, that is, models of order flows, in contrast to classical economic equilibrium theories of utility-maximizing, rational, ``representative'' investors. Mathematically, they are analyzed using tools of functional central limit theorems, strong approximations and weak convergence. Our main examples focus on investor inertia, a trait that is well-documented, among other behavioral qualities, and modelled using semi-Markov switching processes. In particular, we show how inertia may lead to the phenomenon of long-range dependence in stock prices. Comment: To appear in the Handbook of Financial Engineering (Vadim Linetsky and John Birge eds.)