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<p>In this special issue contribution, I provide a personal view on the role of bifurcation analysis of climate models in the development of a theory of climate system variability. The state of the art of the methodology is shortly outlined, and the main part of the paper deals with examples of what has been done and what has been learned. In addressing these issues, I will discuss the role of a hierarchy of climate models, concentrate on results for spatially extended (stochastic) models (having many degrees of freedom) and evaluate the importance of these results for a theory of climate system variability.</p>