T-Duality, Dual Conformal Symmetry and Integrability for Strings on AdS_5 x S^5

In recent years two intriguing observations have been made for N=4 super Yang-Mills theory and for superstrings on AdS5xS5: In the planar limit the computation of the spectrum is vastly simplified by the apparent integrability of the models. Furthermore, planar scattering amplitudes of the gauge theory display remarkable features which have been attributed to the appearance of a dual superconformal symmetry. Here we review the connection of these two developments from the point of view of the classical symmetry by means of a super-T-self-duality. In particular, we show explicitly how the charges of conformal symmetry and of the integrable structure are related to the dual ones.