In this tutorial review we discuss some basic aspects concerning the magnetic properties of rare-earth ions, which are currently the subject of a renovated interest in the field of molecular magnetism, after the discovery that slow relaxation of the magnetization at liquid nitrogen temperature can occur in mononuclear complexes of these ions. Focusing on Dy(III) derivatives a tutorial discussion is given of the relation of the crystal field parameters, which determine the anisotropy of these systems and consequently their interesting magnetic properties, with the geometry of the coordination sphere around the lanthanide centre and with the pattern of f orbitals. The problem of systems of low point symmetry is also addressed by showing how detailed single crystal investigation, coupled to more sophisticated calculation procedures, is an absolute necessity to obtain meaningful structure–property relationships in these systems.