I will discuss a reduction procedure for Courant algebroids, generalized complex, and generalized Kähler structures. In the context of generalized complex structures, this procedure interpolates between holomorphic reduction of complex manifolds and symplectic reduction. Our theory is based on extended notions of group action and moment map, which reflect the enhanced symmetry group of a Courant algebroid. Key examples of generalized Kähler reduced spaces include new explicit bi-Hermitian metrics on $CP^2$. This is joint work with G. Cavalcanti and M. Gualtieri.