Recent theoretical developments in photon-atom scattering

We describe recent developments in the theory of elastic and inelastic photon-atom scattering, considering implications for applications. We discuss what is now understood about the validity of various simpler approaches: when they work and when they don't. In elastic scattering, topics include: (1) edge regions, where more sophisticated descriptions are needed to describe the features, useable in determining composition of materials, (2) anomalous scattering, used in determinations of structure, (3) polarization phenomena, a new tool and (4) Delbrück scattering, addressing light-light scattering. In inelastic scattering, topics include: (1) the validity of impulse approximation, the basis of the determination of atomic momentum density from Compton profiles, (2) resonant Raman scattering and (3) infrared rises and the challenge to experiment. It is now possible to discuss how to characterize and tabulate these cross sections, and to identify where further work is still needed.