In joint work with G. Tian I introduced a natural evolution equation generalizing the Kahler Ricci flow to complex, non-Kahler manifolds.  Moreover we showed that this equation preserves "generalized Kahler geometry."  In this talk I will discuss further results on this flow in the generalized Kahler setting, including a sharp long time existence result for complex surfaces.  These results lead to strong rigidity and classification results for generalized Kahler structures.