Several decades ago, the idea arose that paramagnetic molecules could replace the magnetic particles used in hard disk storage devices, which could allow data densities that were orders of magnitude higher than the state of the art at the time. These investigations started with a dodecanuclear manganese cluster with an S = 10 ground state. This ground state possesses a sizable zero-field splitting (ZFS), resulting in an energy barrier towards inversion of the magnetic moment, and concurrent slow relaxation at low temperatures. Molecules that possess this property have been named single-molecule magnets (SMMs). Because for the simplest case and an integer spin ground state, this energy barrier U eff is given by U eff = DS 2 z with the ZFS constant D and the ground state spin S, much energy was devoted to increasing S. As a result, a great deal of knowledge and understanding of the magnetic properties of high-spin clusters with large magnetic anisotropies, and especially of the interplay between the local ZFS and the isotropic exchange interactions J between the paramagnetic ions were gained. Most data were interpreted in the strong-exchange approximation, i.e., assuming J ≫ D, and the limitations of this model were explored. Because D decreases with increasing S, this approach was doomed to fail in terms of the envisaged practical application.