A theme in the last decade of computational systems biology research has been how molecular noise is a factor that needs to be accounted for, both to understand how gene regulatory networks are able to operate robustly in a noisy molecular environment, but also how noise can drive and enhance the function of regulatory systems and explain phenotypic variability on both the individual cell and population levels. A particularly intriguing question is how both spatial and temporal aspects of intracellular signaling and control contribute to the function. To study this, spatial stochastic methods are needed. They become much more computationally expensive than the corresponding well-mixed models and offer additional challenges on the theoretical level. We develop multiscale and multilevel simulation methods for stochastic reaction-diffusion processes, focusing on geometric flexibility in the models, multiscale and multilevel simulation, fundamental theory for how to model the chemical reaction kinetics, as well the validity of widely used model reductions when applied in a spatial context. We take part in the computational systems biology project.