This talk will discuss aspects of the dynamics and structure of robust heteroclinic networks in globally coupled phase oscillator systems. As recognised by a number of authors, one can readily find dynamics of `slow switching' or `slow oscillations' between cluster states in cases where these heteroclinic networks are attracting. The detailed dynamics becomes rapidly very complicated on increasing the number of oscillators in the system, but it can be modelled by transitions between a number of symmetrically related states. We suggest how this allows one to construct and model coupled dynamical systems that perform reliable discrete computations given very small perturbations to the the system, and we highlight a number of theoretical and practical questions about such systems. (Work with Jon Borresen and Marc Timme).