2d Sigma Models and Geometry

Supersymmetric nonlinear sigma models have target spaces that carry interesting geometry. The geometry is richer the more supersymmetries the model has. The study of models with two dimensional world sheets is particularly rewarding since they allow for torsionful geometries. In this review I describe and exemplify the relation of 2d supersymmetry to Riemannian, complex, bihermitian, (p,q) hermitean, K¨ahler, hyperk¨ahler, generalised geometry and more.