We will discuss in this survey article a new framework for analysing computations on time series and in particular on spike trains, introduced in (Maass et. al. 2002). In contrast to common computational models this new framework does not require that information can be stored in some stable states of a computational system. It has recently been shown that such models where all events are transient can be successfully applied to analyse computations in neural systems and (independently) that the basic ideas can also be used to solve engineering tasks such as the design of nonlinear controllers. Using an illustrative example we will develop the main ideas of the proposed model. This illustrative example is generalized and cast into a rigorous mathematical model: the Liquid State Machine. A mathematical analysis shows that there are in principle no computational limitations of liquid state machines in the domain of time series computing. Finally we discuss several successful applications of the framework in the area of computational neuroscience and in the field of artificial neural networks.