Complex behaviour in many biological systems arises from the stochastic interactions of spatially distributed particles or agents. Examples range from gene expression to chemotaxis and epidemiology. Stochastic reaction-diffusion processes are widely used to model such systems, yet they are notoriously difficult to simulate and calibrate to observational data. In this talk, I will show how joint time marginals of stochastic reaction-diffusion processes can be approximated by spatio-temporal Cox processes, a well-studied class of models from computational statistics. The resulting approximation allows us to naturally define an approximate likelihood, which can be efficiently optimised with respect to the kinetic parameters of the model. We show on several examples from systems biology and epidemiology that the method yields consistently accurate parameter estimates, and can be used effectively for model selection.