Many physical situations involve the interplay of different phenomena at different scales. The corresponding description requires the use of multi-physics models, whose mathematical formulation poses several challenges. Examples are found in the classical-quantum coupling in molecular dynamics or in the coupling between mean flow and fluctuation kinetics in turbulence. In plasma physics, the interaction of energetic particles (obeying kinetic theory) with a fluid bulk (obeying magnetohydrodynamics) requires formulating hybrid kinetic-fluid models, which are often obtained by making assumptions that destroy the correct energy balance. This talk shows how momentum-map techniques in geometric mechanics provide a powerful unifying framework for both kinetic-fluid and classical-quantum coupling, thereby leading to new hybrid models in different contexts.