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In three space-time dimensions,N-extended anti-de Sitter (AdS) supersymmetry exists in several incarnations labeled by two non-negative integers p and q such that p+q =N.Different types of AdS supersymmetry lead to drastically different restrictions on the target space geometry of supersymmetric nonlinear sigma models.This talk will review the structure of nonlinear sigma models in (p,q) AdS supersymmetry.