The description of basic experiments of the rare-earth hard magnetic materials, high-field magnetization curves on single-crystalline samples of Ho2Co17 and Nd2Fe14B is reviewed with the aim to derive parameters physically relevant on atomic scale. The anisotropic, magnetic properties have been found to be of single-ion origin. The successful description of the rare-earth compounds Ho2Co17, Nd2Fe14B, Pr2Fe14B, ErNi5, PrRu2Si2, ErRu2Si2 in terms of the crystal-field, spin-orbit and inter-site magnetic interactions proves the existence, in a solid, the discrete atomic-like low-energy electron structure that predominantly governs the magnetic and electronic properties. The macroscopic properties have been correlated with the atomic-scale parameters. These studies reveal the importance of the low-symmetry crystal-field interactions (high-order charge multipolar interactions) in description of the magnetic properties of 4f compounds. (C) 2002 Elsevier Science B.V. All rights reserved.