The polar stratosphere is critically affected by ozone depletion and its recovery, as well as by increasing concentrations of greenhouse gases. Recent cold Arctic stratospheric winters have experienced record low temperatures and correspondingly large ozone depletion, raising the question whether the cold Arctic stratospheric winters are getting colder and whether or not this may be related to increasing greenhouse gas concentrations. In my presentation I will review the evidence based on observations of polar stratospheric temperatures and ozone depletion, together with expected changes based on climate model simulations.