Non-local operators in the time variable are used to model anomalous diffusion, where a particle plume spreads at a rate that is inconsistent with the classical model. And, non-local space operators describe long-range jumps and interactions of the given diffusion. Compared to PDE theory, which is relatively well-developed for a wide class of non-local operators, Stochastic PDE theory has been successful only for non-local space operators of few special types. Hence for the description of various complex phenomena, it becomes essential to develop the theory of SPDEs with general non-local operators. In this talk, we present the uniqueness, existsnce and regularity theory for stochastic PDEs with such nonlocal operators.