In this talk, I am going to give an overview of recent results I have obtained with a number of colleagues to work towards a more coherent dynamical systems theory for stochastic partial differential equations (SPDEs). This includes basic results regarding existence, regularity, steady states, bifurcations, attractors, center manifolds, and multiscale dynamics. In this talk I shall particularly focus on invariant manifolds, and how we want to lift techniques from deterministic analysis as much as possible to the stochastic setting.