Our understanding of the ozone hole involves not only stratospheric chemistry and electromagnetic radiation (solar and terrestrial) but also a highly inhomogeneous “wave-turbulence jigsaw” in which wavelike regions, and turbulent or vortical regions, fit together both geometrically and dynamically. This is outside the scope of standard homogeneous-turbulence theory. The edge of the ozone hole is a wavelike region and is one of the climate system's great jetstreams. Other examples include the atmospheric tropopause jets that steer cyclonic storms and bring us mild or severe winters, and narrow ocean currents like the Gulf Stream, the Kuroshio, and the Agulhas. These are all strong jets, whose wavelike nature mediates their characteristic meandering behaviour. Their cores are marked by concentrated horizontal gradients of a fundamental material invariant, the Rossby-Ertel potential vorticity (PV). The jets behave anti-frictionally in that they tend to narrow or self-sharpen their velocity profiles when their natural meandering behaviour is excited. The meanders are guided Rossby waves whose dispersion properties encourage them to break sideways on the flanks of the jet, producing piecewise turbulent mixing of the PV, on either side but not across the core. The recognition and eventual understanding of this anti-frictional or anti-diffusive behaviour was part of a great paradigm change regarding the nature of large-scale momentum transport in atmospheric and oceanic flows. Jets behave somewhat like the veins and arteries of the climate system in that they transport chemicals rapidly downstream, but inhibit cross-jet transport. That is why the ozone hole has a sharp edge, with different chemical compositions on either side.