The Sun exhibits waves, oscillations, and instabilities on a wide range of timescales. Modern observations from space and ground-based instruments reveal these phenomena with unprecedented spatial, spectral, and temporal resolutions. Such observations have also driven rapid advancements in the theoretical modelling of key physical processes. These models are also increasingly being used to explain observations of oscillations or quasiperiodic pulsations associated with other stars. We aim to bring together experts in the solar and stellar communities, review recent advances in the field, and discuss ways to further advance our understanding of astrophysical plasma dynamics.