In many transition metal dihydrides and dihydrogen complexes the hydrogens are relatively weakly bound and exhibit a fairly high mobility, in particular with respect to their mutual exchange. Part of this high mobility is due to the exchange symmetry of the two hydrogens, which causes an energy splitting into even and odd spatial energy eigenfunctions, resulting in the typical coherent tunneling of a two-level system. Owing to the quantum mechanical symmetry selection principles the eigenfunctions are connected to the possible nuclear spin states of the system. If the tunneling frequency is in the proper frequency window it is thus possible to observe these tunneling transitions by NMR at very low temperatures, where no thermally induced exchange reactions overshadow the tunneling. The first part of this review gives an introduction into the interplay of chemical kinetics and tunneling phenomena in general, rotational tunneling of dihydrogen in a two-fold potential in particular and the Bell tunnel model, followed by a summary of solid state NMR techniques for the observation of these tunnel processes. Then a discussion of the effects of these processes on the 2H NMR line shape is given. The second part of the review reports results of a 2H-solid state NMR spectroscopy and T1 relaxatiometry study of trans-[Ru(D2)Cl(PPh2CH2CH2PPh2)2]PF6, in the temperature regime from 5.4 to 320 K. In the Ru-D2 sample coherent tunneling and incoherent exchange processes on the time scale of the quadrupolar interaction are observed. From the spectra and T1-data the height of the tunneling barrier is determined. Next results of 2H-spin–lattice relaxation measurements for a selectively η2 − D2 labeled isotopomer of the complex W(PCy3)2(CO)3)(η2 − D2) are presented and discussed. The relaxation measurements are analyzed in terms of a simple one dimensional Bell tunnel model and comparison to incoherent neutron scattering (INS) data from the H2 complex. The comparison reveals a strong isotope effect of 2 × 103 for the exchange rates of the deuterons versus hydrons.