We review recent experimental and theoretical studies of the non-local plasmon dispersion relations of both single and double layers of graphene which are Coulomb-coupled to a thick conducting medium. High-resolution electron energy loss spectroscopy (HREELS) was employed in the investigations. A mean-field theory (R.P.A.) formulation was used to simulate and explain the experimental results, with the undamped plasmon excitation spectrum calculated for arbitrary wave number. Our numerical calculations show that when the separation a between a graphene layer and the surface is less than a critical value a c  = 0.4k F −1 , the lower acoustic plasmon is overdamped. This result seems to explain the experimentally observed behavior for the plasmon mode intensity as a function of wave …