When electron spins of nanoparticles are ferromagnetically coupled, they normally form a single domain with a large magnetic moment which may have a fixed orientation in the cluster, resulting in hysteresis behaviour in their magnetisation curves. Above the so-called blocking temperature these coupled moments behave like individual spins, which is called super-paramagnetism. Smaller clusters with a high spin embedded in a non-magnetic environment are magnetic quantum systems which show stepped hysteresis curves. Also, metal nanoparticles of non-magnetic elements such as Pt, Pd or Au and even oxides like ZnO become paramagnetic at low temperatures because of their uncompensated spins at or near the surface. In contrast, metal particles show super-diamagnetic behavior at room temperature. Interesting magnetic order phenomena emerge near planar surfaces or interfaces, or for chains of coupled magnetic atoms.