Oscillatory dynamics pervades the universe, appearing in systems of all scales. Whilst autonomous oscillatory dynamics has been extensively studied and is well understood, the very important problem of non-autonomous oscillatory dynamics is less well understood. Here, we provide a framework for non-autonomous oscillatory dynamics, within which we can define intermittent phenomena such as intermittent phase synchronisation. Moreover, we demonstrate this framework with a coupled pair of non-autonomous phase oscillators as well as a higher-dimensional system comprising of two interacting phase-oscillator networks. •A new framework for phase-dynamics phenomena in non-autonomous oscillatory systems.•Interactions between pairs of non-autonomous oscillators and networks are considered.•Intermittent synchronisation is formulated mathematically.•Relevant for many real-world problems.