A basic problem in surface science is that, unlike bulk materials, very few of the atomic scale structures are known despite many years of effort. Even the advent of STM has not helped that much since it is difficult to impossible to interpret images without a-priori information. Transmission electron diffraction (or x-ray diffraction) data from surfaces represent a unique opportunity for the application of Direct Methods to solve surface structures, opening up new avenues for science. Diffraction from a surface when the bulk is only weakly dynamical is at least 90% kinematical, but it may be the case that strong (surface) scattering is buried under bulk reflections including the lxl or “surface forbidden bulk-allowed” reflections. In addition, further out in the diffraction pattern subsurface relaxation effects become very important, and these cannot be considered using conventional Direct Methods; instead of sharp atomic-features the true exit wave will have small positive/negative dipoles.