Among the different dynamical processes that take place in polymers, methyl group rotation is perhaps the simplest one, since all the relevant interactions on the methyl group can be condensed in an effective mean-field one-dimensional potential. Recent experimental neutron scattering results have stimulated a new revival of the interest on methyl group dynamics in glasses and polymer systems. The existence of quantum rotational tunnelling of methyl groups in polymers was expected for a long time but only very recently (1998), these processes have been directly observed by high-resolution neutron scattering techniques. This paper revises and summarizes the work done on this topic over last ten years by means of neutron scattering. It is shown that the results obtained in many chemically and structurally different polymers can be consistently described in the whole temperature range -- from the quantum tunnelling limit to the classical hopping regime -- as well as in the librational spectrum, in terms of the Rotation Rate Distribution Model (RRDM), which was first proposed in 1994. This model introduces a distribution of potential barriers for methyl group rotation, which is associated to the disorder present in any structural glass. The molecular and structural origin of the barrier distribution in polymers is discussed on the basis of a huge collection of investigations reported in the literature, including recent fully atomistic molecular dynamics simulations. ; Comment: Review article to be published in Progress in Polymer Science. 45 pages and 29 figures