Neutron scattering techniques such as quasi-elastic neutron scattering, QENS, have proven to be well-suited tools for studying structure and dynamics of surface adsorbed molecules. In contrast to many more widely used surface science techniques neutron scattering allows the microscopic characterization of samples under a wide range of thermodynamic conditions, as the samples are not constrained to ultra high vacuum environment. Moreover, neutron scattering allows the separation of coherent and incoherent scattering, giving access to different diffusive mechanisms such as single particle diffusion, mass transport, rotations, or vibrations. In this paper we will review recent progress and the state-of-the-art in neutron scattering experiments on surface adsorbed molecules in the sub-monolayer coverage range with a specific emphasis on studies of carbon and other high surface density substrates. We will also cover recent progress in theoretical modeling, since the usefulness of neutron scattering data on surface dynamics can be strongly enhanced by computational modeling, such as molecular dynamics (MD) simulations and the development of analytical models.