Stochastic modelling and simulation of intracellular processes offer many challenges, especially if the spatial aspects are deemed to be important. In this talk we will give a brief overview of one of the frameworks for spatial stochastic simulations, the Reaction-Diffusion Master Equation (RDME), and illustrate how it can be used to model intracellular signalling and gene regulation. We will also briefly describe some of the computational issues that arise due to the multiscale nature of intracellular reaction-diffusion processes, as well as some of the approaches we have taken to address those issue. Finally, we will introduce PyURDME, a new programming interface to URDME in Python, and MOLNs, a cloud-computing platform for large scale computational experiments and model analysis using PyURDME.