This review summarizes experimental evidence for the freezing of reorienting moments in solids. The moments may be of dipolar or quadrupolar nature, or both; they belong to one of the constituents of a mixed-crystal solid. Extensive results are reported for the following systems: KCl doped with hydroxyl, potassium tantalate doped with Li, Na and Nb, alkali halide cyanides and alkali-alkali cyanides, rubidium ammonium dihydrogen phosphate, solid ortho-para hydrogen and argon-nitrogen mixtures. These have clearly glass-like properties. In other systems, results are limited to one or two methods hinting at glass formation; some of those are also reported. Clustering phenomena and the slow-down of reorientations at the freezing temperature are observed in susceptibility measurements and by local probing on nuclear spins. The modulation of the structure by cluster formation is revealed by diffraction experiments. These phenomena are confronted with model predictions and numerical simulations. © Taylor & Francis Group, LLC.