We begin our presentation with a brief description and comparison of these leading modes of hemispheric variability with an emphasis on their respective roles in polar climate variability and change. Following this we address the important issue of whether or not these modes are in fact the best description of hemispheric variability and change. The AO and AAO are usually obtained using linear principal component analysis which produces the optimal, although somewhat restrictive, linear approximation to the data. In an attempt to overcome this limitation we apply the recently introduced nonlinear principal component analysis which finds the optimal nonlinear approximation to the data. It is shown for example that Northern Hemispheric SLP variability is best characterized by three distinct quasi-stationary states, to which the AO is the best linear compromise. One of the regimes, for example, is reminiscent of the negative phase of the North Atlantic Oscillation which the analysis shows displays a substantial downward trend in its frequency of occupation. Interestingly, this observed downward trend can be reproduced with a global climate model subject to enhanced greenhouse gas forcing. We conclude the presentation by characterizing the leading Northern and Southern Hemisphere nonlinear regimes of variability with an emphasis on their respective roles in polar climate variability and change.