The stellar disc of the Milky Way exhibits clear departures from planarity, the most conspicuous manifestation being the Galactic Warp but also includes an apparent corrugation pattern in number counts around 15kpc from the Galactic centre, a wave like pattern in the vertical velocities of stars as a function of guiding radius, asymmetries about the midplane in both number counts and bulk motions, and phase spirals in the z–vz projection of the local stellar distribution function. We discuss the physics of these phenomena and, in particular, suggest a possible avenue for inferring the vertical force in the Solar Neighbourhood from phase spirals. We apply Dynamic Mode Decomposition, a technique widely used in the realm of fluid mechanics, to simulations of disc galaxy simulations. This method appears to be particularly well-suited to the study of nonlinear processes such as the coupling of warps and spirals, first discussed by Masset and Tagger.