The possibility of obtaining spin glasses by addition of impurities in an antiferromagnetic insulator is examined. Dipolar interactions are briefly considered but the attention is focussed on Heisenberg systems. Equivalence with the Edwards-Anderson model is derived in a theoretical case. Experimental realisations, such as quasi-one dimensional systems, and spinels, are reviewed. A weak concentration of non-magnetic impurities can give rise to a new state that we call “semi spin glass”, in which a ferromagnetic component coexists with a transverse, spin glass component. An important case is when the pure system has a high ground state degeneracy (cooperative paramagnet). Non-magnetic impurities or other forms of disorder can transform it into a spin glass.