Computation is often thought of as a branch of discrete mathematics, using the Turing model. That model works well for conventional applications such as word processing, database transactions, and other discrete data processing applications. But much of the world’s computer power resides in embedded devices, sensing and controlling complex physical processes in the real world. Other computational models and paradigms might be better suited to such tasks. For example, a computer can be regarded as a form of open dynamical system. One particular approach taking this view is reservoir computing, which can be instantiated in a range of different material substrates. This approach can support smart processing ‘at the edge’, allow a close integration of sensing and computing in a single conceptual model and physical package, and provides a uniform approach to building hybrid architectures of heterogeneous devices.