The principles of Surface Organometallic Chemistry are reviewed and general rules governing the reactivity of organometallic complexes with the active sites on surfaces of oxides, zeolites or metals are given. The subsequent stoechiometry reactivity of these surface species has also been studied and shown to be comparable to that usually observed in classical organometallic chemistry with the same elementary steps. In each case, some examples are given. Finally, some applications of these surface complexes in heterogeneous catalysis are listen, with emphasizing the structure-activity relationship.