The present-day response of a Galactic disc stellar population to a non-axisymmetric perturbation of the potential, in the form of a bar or spiral arms, can be treated, away from the main resonances, through perturbation theory within the action-angle coordinates of the unperturbed axisymmetric system. The first order moments of such a perturbed distribution function (DF) in the presence of spiral arms give rise to non-zero radial and vertical mean stellar velocities, called breathing modes. Such an Eulerian linearized treatment however diverges at resonances. The Lagrangian approach to the impact of non-axisymmetries at resonances avoids this problem. It is based on the construction of new orbital tori in the resonant trapping region, which come complete with a new system of angle-action variables. These new tori can be populated by phase-averaging the unperturbed DF over the new tori. This boils down to phase-mixing the DF in terms of the new angles, such that the DF for trapped orbits only depends on the new set of actions. This opens the way to quantitatively fitting the effects of the bar and spirals to Gaia data with an action-based DF.