Metal vapor deposition to form ohmic contacts is commonly used in the fabrication of organic electronic devices because of significant manufacturability advantages. In the case of single molecular layer devices, however, the extremely small thickness, typically ~1-2nm, presents serious challenges in achieving good contacts and device integrity. This review focuses on recent scientific aspects of metal vapor deposition on monolayer thickness molecular films, particularly self-assembled monolayers, ranging across mechanisms of metal nucleation, metal-molecular group interactions and chemical reactions, diffusion of metal atoms within and through organic films, and the correlations of these and other factors with device function. Results for both non-reactive and reactive metal deposition are reviewed. Finally, novel strategies are considered which show promise for providing highly reliable and durable metal/organic top contacts for use in metal-molecule-metal junctions for device applications.