Aust. J. Phys., 1985,38, 371-404 Theoretical and experimental techniques for the determination of the X-ray anomalous dispersion corrections f'(w, LI) and fl/(w, LI) are discussed. The results of experiments on metallic, ionic and covalently bonded materials typified by copper and nickel, lithium fluoride, and silicon respectively are compared with the theoretical predictions. Attention is drawn to deficiencies in both the experimental and the theoretical approaches.