The question of how to reconcile Connes's theory of spectral triples with the theory of quantum groups has been the subject of intense investigation over the last 30 years. Despite this we are still quite far from a proper understanding of how the two areas interact. What has become clear, however, is that quantum group homogeneous spaces are more tractable than quantum groups themselves. This can roughly be understood as the worst of the noncommutative behaviour being quotiented out. In this talk, we focus on the case of the quantum flag manifolds, discussing how their classical Kahler geometry admits a remarkable direct q-deformation. We then show how the associated Dirac-Dolbeault operator can be completed to give a spectral triple, directly q-deforming the commutative spectral triple of the flag manifolds.