Discrete subgroups of SLn(R) are called Anosov if they exhibit "good" eigenvalue growth properties, which persist under small deformation. This makes them suitable higher-rank generalizations of convex-cocompact Fuchsian groups, which have a rich ("Teichm?ller" or "Fricke-Klein") deformation theory. In this talk, we will try to answer the question: what are the possible directions in which the tuple of eigenvalues can grow? What are the most extreme directions, and which group elements achieve them? Thurston's results on the Lipschitz distance in Teichm?ller space give a surprisingly intricate answer in a special case. Guided by these, we will describe some generalizations and challenges in the general case. Joint work with J.Danciger and F.Kassel.