There are many intracellular signalling pathways where the spatial distribution of the molecular species cannot be neglected. These pathways often contain negative feedback loops and can exhibit oscillatory dynamics in space and time. One such class of pathways is those involving transcription factors (e.g. Hes1, p53-Mdm2, NF-kB, Heat-shock proteins). In this talk, results from recent mathematical models which have been used to study the spatio-temporal dynamics of intracellular systems will be presented. Using the Hes1 gene regulatory network as an exemplar, both phenomenological partial differential equation models and mass action based spatial stochastic models will be considered. The benefits and drawbacks of the two different approaches will be discussed. For the partial differential equation approach, I will show how the diffusion coefficient can act as a bifurcation parameter, which, if in a certain range, can drive oscillatory dynamics.