in this talk we define the fundamental geometric constructions behind the generalized kahler geometry introduced by hitchin and gualtier and set up an appropriate generalization of the calabi problem. similarly to cao's approach to the solution of the classical calabi problem, we study the existence and convergence of the generalized kahler-ricci flow (gkrf) on relevant backgrounds. in particular, we prove that on a kahler calabi-yau background, the gkrf converges to the unique classical ricci-flat structure. this result has non-trivial applications to understanding the space of generalized kahler structures, and as a special case yields the topological structure of natural classes of hamiltonian symplectomorphisms on hyperkahler manifolds. based on a joint work with apostolov, fu and streets.