The first observations 30 years ago of molecular clustering via quantum diffusion in solidH2in nuclear magnetic resonance (NMR) and pressure experiments are described. A previous review on quantum diffusion and tunneling up to 1986 is updated to reflect progress in the last ten years. In particular I review the effect of clustering on heat capacity in solidD2and on the thermal conductivity in solidH2.The configurational relaxation time observed inD2at 1.75 K is found to scale with that inH2at the same temperature in terms of the predictions of ortho–para resonant conversion-induced hopping. The relaxation times measured simultaneously on the same sample in NMR and conductivity experiments reflect different configurational processes. The theory of molecular hopping and pairing in solidH2is outlined and compared with experiments. The tunneling frequency of HD in solidH2deduced from transverse and longitudinal NMR relaxation experiments between 0.03 and 14 K is discussed. The hopping of ortho-H2,invoked as a mechanism in the enhanced ortho–para conversion in presence ofO2impurities, is mentioned. Finally, recent tunneling results for H, D andH2−anions in solidH2during the studies of low temperature reaction dynamics are also briefly described. In the Appendix, the hopping frequency determination in HD from NMR transverse relaxation time measurements is reviewed. ©1998 American Institute of Physics.