Curved-wave multiple-scattering (MS) theory provides a unified treatment of XAFS, encompassing both EXAFS and XANES, as well as a formal equivalence between exact treatments and the (MS) expansion carried to all orders. Recent developments in the theory of XAFS are reviewed with an emphasis on progress in curved-wave MS calculations and on understanding the nature of MS contributions in EXAFS and XANES. In particular we discuss a unified ab initio MS treatment of XAFS based on a scattering matrix formalism which has sufficient speed and accuracy to treat high-order MS in extended systems. We find that neither low-order MS nor full MS theories are fully satisfactory. Instead, sufficiently high-order MS appears to be necessary for the convergence of both EXAFS and XANES calculations. Our approach also gives a MS interpretation of the σ* shape-resonances observed in XANES. We demonstrate that these peaks result from coherent, high-order MS. We also obtain a generalization of the Natoli rule correlating the resonance locations with bond length.