The principal purpose of this paper is to provide a review of the Fractal Market Hypothesis (FMH) which is a hypothesis for analysing financial time series based on the principles of fractal geometry, specifically the self-affine properties of stochastic fields. However, this paper has also been composed for readers who have no or little prior knowledge of fractal geometry or the principles of financial time series modelling, risk assessment analysis and future price prediction. For this reason, this paper provides a short introduction to fractal geometry and an overview on the mathematical modelling of financial signals. These elements are then combined to explain the principles of the FMH and how and why it can be used to model financial times series data. The FMH is part of the continuing evolution of ‘technical’ market theory, and, in this section, we provide a contextual overview of some of the basic concepts relating to the study of market risk, presenting the ideas that lie behind the developments in the field that have led to the FMH and its applications.