I will introduce Generalized Para-Kahler geometry, its relationship to supersymmetry and para-Hermitian geometry, which is a geometry that naturally describes certain cases of T-duality. I will also discuss new examples of topological sigma models that are described by above geometries and comment on a possible connection to mirror symmetry. If time permits, I will explain my work in progress, which relates para-Hermitian and Generalized Kahler geometry.