Over the past few years two new descriptive terms have entered the lexicon of magnetism: spin glass and mictomagnet. Both of these terms apply to non‐dilute magnetic alloys where there is a random freezing of impurity moments at a distinct temperature which gives rise to a sharp peak in the low field susceptibility and a sudden splitting of the Mössbauer spectrum, along with remanence, irreversibility and relaxation. Spin glass refers mainly to the lower concentration regime where the long range indirect RKKY interaction is responsbile for the cooperative freezing of the spins. Mictomagnetism is more appropriate in describing the magnetic clusters which form in the spin glass matrix at higher concentrations, due to local (first or second nearest neighbor) exchange, or when there is a tendency towards short range atomic ordering. The present paper will attempt to illustrate this type of random magnetism: (1) by presenting a variety of known (and conjectured) alloy systems which exhibit such characteristics, (2) by reviewing the salient experimental features of the susceptibility, magnetization, Mössbauer effect, neutron scattering, resistivity, thermopower and the specific heat, and (3) by surveying the development of theoretical models to treat these effects.