In this paper we review some recent models for gas-surface scattering in which the gas particle can interact and exchange energy with the vibrational modes of the solid. Probabilities for energy transfer and sticking are computed tor He. Ne, and Ar incident on a Cu surface, for a number of particle energies and surface temperatures. All of the models are applied to the same set of systems, and the results are compared. In all cases the lattice vibrations are treated quantum mechanically. A close-coupling approach which includes only single-phonon processes is presented. It is accurate tor He and H-2, and Ne at low energies and temperatures. Two common approaches to the problem based on an uncorrelated particle bath state, the forced oscillator and time dependent Hartree method, are discussed. They are compared with each other and with the close-coupling calculation in the one-phonon limit. Mean field approaches which attempt to improve upon these zero-correlation models are presented and compared with the above models. A one-phonon multiconfiguration self consistent field model is also presented. The nature of atom- surface sticking is examined over a wide range of energies, temperatures, and masses.