We discuss the effect of vacuum polarization on the propagation of photons in curved spacetime in QED. A compact formula is presented for the full frequency dependence of the refractive index for any background in terms of the Van Vleck-Morette matrix for its Penrose limit. This shows explicitly how the superluminal propagation found in the low-energy effective action is reconciled with causality. The geometry of null geodesic congruences is found to imply a novel analytic structure for the refractive index and Green functions of QED in curved spacetime, which preserves their causal nature but violates familiar axioms of S-matrix theory and dispersion relations. The Kramers-Kronig dispersion relation and the optical theorem for QFT in curved spacetime are discussed critically. The significance of the Penrose limit for black hole spacetimes and their relation to homogeneous plane waves is explained and unexpected features of light propagation in a number of spacetimes are described.