  Many Ramond-Ramond backgrounds which arise in the AdS/CFT correspondence are
described by integrable sigma-models. The equations of motion for classical
spinning strings in these backgrounds are exactly solvable by finite-gap
integration techniques. We review the finite-gap integral equations and
algebraic curves for coset sigma-models, and then apply the results to the
AdS(d+1) backgrounds with d=4,3,2,1.
