This talk will discuss ongoing research to understand practical aspects of the behaviour of non-autonomous systems (ie dynamical systems where the rules of evolution that change with time). Although non-autonomous systems are well studied, it remains hard to make general statements about attracting behaviour without limiting to a specific category. Such a category is the class of asymptotically autonomous systems, where there are autonomous past and future limits. Using the concepts of pullback attractor it is possible to understand sudden changes are often termed tipping points. Particularly interesting consequences relate to predictability of ensembles in cases where the past limit attractor is chaotic, and a concept of a nonautonomous physical measure is needed. We discuss applications to the dynamics of simple climate models.