In both rare‐earth and transition‐metal salts there may be appreciable interactions of high degree in the orbital or total spin angular‐momentum operators acting between the ions. These interactions may arise either from the exchange interaction between the electrons or from the electrostatic coupling between the electric multipole moments of the two atoms. The latter in turn may arise either directly through the multipole coulombic field or indirectly through the coupling of the ions to the lattice. In transition‐metal compounds the orbital moment is usually quenched, so that for interactions involving only the ground multiplet, the anisotropy introduced by the orbital effects is quite small. However, in rare‐earth insulators the rare‐earth magnetic moment has appreciable orbital content, so that the high‐rank interactions are of considerable importance. In this paper we give a brief discussion of the theory of these interactions, and we then review recent experimental work on rare‐earth compounds in which these effects have been shown to be important. Particular emphasis is given to: (a) experiments on YIG which indicate the presence of appreciable high‐degree exchange; (b) experiments on the EPR of pairs of coupled Ce3+and Nd3+ions in LaCl3and LaBr3; in these experiments it was possible both to measure the electric quadrupole‐quadrupole interaction and to isolate contributions to the interaction tensors from high‐degree exchange of the formJ+5(1)J−5(2) andJxl(1)J±5(2); (c) a series of experiments and calculations on UO2which indicate the presence of appreciable electric multipole coupling via the lattice.