Imbalance refers to the departure from the large-scale primarily vortical flows in the atmosphere and ocean whose motion is governed by a balance between Coriolis, pressure-gradient and buoyancy forces, and can be described approximately by quasi-geostrophic theory or similar balance models. Imbalanced motions are manifest either as fully nonlinear turbulence or as internal gravity waves which can extract energy from these geophysical flows but which can also feed energy back into the flows. Capturing the physics underlying these mechanisms is essential to understand how energy is transported from large geophysical scales ultimately to microscopic scales where it is dissipated. In the atmosphere it is also necessary for understanding momentum transport and its impact upon the mean wind and current speeds. During a February 2018 workshop at the Banff International Research Station (BIRS), atmospheric scientists, physical oceanographers, physicists and mathematicians gathered to discuss recent progress in understanding these processes through interpretation of observations, numerical simulations and mathematical modelling. The outcome of this meeting is reported upon here.