Chemistry on solid surfaces is central to many areas of practical interest such as heterogeneous catalysis, tribology, electrochemistry, and materials processing. With the development of many surface-sensitive analytical techniques in the past decades, great advances have been possible in our understanding of such surface chemistry at the molecular level. Earlier studies with model systems, single crystals in particular, have provided rich information about the adsorption and reaction kinetics of simple inorganic molecules. More recently, the same approach has been expanded to the study of the surface chemistry of relatively complex organic molecules, in large measure in connection with the selective synthesis of fine chemicals and pharmaceuticals. In this report, the chemical reactions of organic molecules and fragments on solid surfaces, mainly on single crystals of metals but also on crystals of metal oxides, carbides, nitrides, phosphides, sulfides and semiconductors as well as on more complex models such as bimetallics, alloys, and supported particles, are reviewed. A scheme borrowed from the organometallic and organic chemistry literature is followed in which key examples of representative reactions are cited first, and general reactivity trends in terms of both the reactants and the nature of the surface are then identified to highlight important mechanistic details. An attempt has been made to emphasize recent advances, but key earlier examples are cited as needed. Finally, correlations between surface and organometallic and organic chemistry, the relevance of surface reactions to applied catalysis and materials functionalization, and some promising future directions in this area are briefly discussed.