Two new different stochastic models for earthquake occurrence are discussed. Both models are focusing on the spatio-temporal interactions between earthquakes. The parameters of the models are estimated from a Bayesian updating of priors, using empirical data to derive posterior distributions. The first model is a marked point process model in which each earthquake is represented by its magnitude and coordinates in space and time. This model incorporates the occurrence of aftershocks as well as the build-up and subsequent release of strain. The second model is a hierarchical Bayesian space-time model in which the earthquakes are represented by potentials on a grid. The final ambition of the models is to make predictions on the occurrence of earthquakes.