Many cellular and subcellular biological processes can be described interms of diffusing and chemically reacting species, for example, problems in developmental biology, genes and enzymes. Such reaction-diffusion processes can be mathematically modelled using either deterministic partial-differential equations or stochastic simulation algorithms. Stochastic models provide a more detailed understanding of the reaction-diffusion processes. Such a description is often necessary for the modelling of biological systems where small molecular abundances of some chemical species make deterministic models inaccurate or even inapplicable. Stochastic models are also necessary when biologically observed phenomena depend on stochastic fluctuations, for example, switching between two favourable states of the system. There are several stochastic (molecular-based or mesoscopic) approaches for modelling chemical reactions and molecular diffusion. Coupling models of these two fundamental processes together offers several challenging mathematical problems. The goal of this research area is to design reliable, correct and efficient methods for the stochastic simulation of reaction-diffusion processes in biology.