The realization that both the worldsheet theory on AdS_5xS^5 and N=4 SYM can, in certain limits, be be described by integrable systems has lead to a good deal of recent progress in understanding the AdS/CFT correspondence. This talk will review the perturbative construction of the worldsheet S-matrix in the light-cone gauge and discuss the realization of the global symmetries on asymptotic states. A mild non-locality of the supercharges results in the natural appearance of a non-trivial coproduct and we will outline how the symmetries form a Hopf algebra. At leading order this scattering matrix can be compared with the conjectured all-loop asymptotic S-matrix that enters the Bethe equations for gauge theory anomalous dimensions and it will shown that they are in good agreement. This S-matrix provides a convenient description of the two theories and should eventually allow us to compare the complete spectrum on both sides of the duality. Further, we will outline some partial resutls in extending this equivalence, and the corresponding integrable structures, to include worldsheet quantum loop effects.