The quasi-elastic neutron scattering (QENS) technique was first used to derive self-diffusivities of hydrocarbons in zeolites, but transport diffusivities of deuterated molecules and of molecules which do not contain hydrogen atoms can now be measured. The technique allows to probe diffusion over length scales ranging from an Å to hundreds of Å. The mechanism of diffusion can thus be followed from the elementary jumps between adsorption sites to Fickian diffusion. Since the space and time scales of the neutron techniques match closely the ones covered by molecular simulations, one expects, and usually finds, good agreement between neutrons and simulations. The neutron data give therefore reference values, so that lower values obtained by other techniques measuring diffusion over longer length scales have to be explained by additional transport barriers.