  We review the recent approaches to modelling financial markets based on
multi-agent systems. After a brief summary of the basic stylised facts observed
in real-market time-series we discuss some simple agent-based systems which are
currently used to model financial markets. One of the most prominent examples
is here the Minority Game (MG), which we address in some more detail. After a
brief discussion of its basic setup and general phenomenology we summarise the
main findings of the statistical mechanics analysis and discuss the emergence
of stylised facts in extensions of the MG near their phase transitions between
efficient and predictable regimes. We then turn towards more realistic variants
which comprise heterogeneous populations of agents, with different memory
capabilities, different inclinations to trade and varying expectations on the
future evolution of the market. Finally we give a short outlook on potential
future work in this area.
