Abstract An introductory survey on applications of high-resolution neutron spectroscopy is presented, dealing with the motion of hydrogen in solids, namely concerning (i) random rotational motions or stationary tunneling states of NH+4-ions or CH3-groups, and (ii) diffusion of hydrogen in alloys. For the rotation of hydrogenous groups in solids, at higher temperatures rotational jumps can be found, whereas quantum states are observed by μeV-spectroscopy at temperatures below 50 K. On the other hand, hydrogen diffusion does not reveal pronounced evidence of quantum effects, except for hydrogen in a metal containing impurity atoms.