A brief review of supersymmetric non-linear sigma models and generalized complex geometry

This is a review of the relation between supersymmetric non-linear sigma models and target space geometry. In particular, we report on the derivation of generalized Kähler geometry from sigma models with additional spinorial superfields. Some of the results reviewed are: Generalized complex geometry from sigma models in the Lagrangian formulation; Coordinatization of generalized Kähler geometry in terms of chiral, twisted chiral and semichiral superfields; Generalized Kähler geometry from sigma models in the Hamiltonian formulation. Contribution to “The 26th Winter School GEOMETRY AND PHYSICS”, Czech Republic, Srni, January 14 21, 2006