This paper reviews the treatment of high-frequency Thomson scattering in the non-relativistic and near-relativistic regimes with the primary purpose of understanding the nature of the frequency redistribution correction to the differential cross-section. This correction is generally represented by a factor involving the ratio ω α /ω β of the scattered (α) to primary (β) frequencies of the radiation. In some formulae given in the literature, the ratio appears squared, in others it does not. In...