Forty years ago, Robert Crabtree published an important paper in square-planar iridium(I) complexes area, and where the hexafluorophosphate of (eta(4)- cycloocta-1,5-diene)(pyridine-kappa N)(tricyclohexylphosphine-kappa P)iridium(I) is very remarkable, showing excellent catalytic performances in the reactions of hydrogenation of highly substituted olefins. This compound, known as the "Crabtree's catalyst", offers many opportunities in Organometallic Chemistry and, in Organic Chemistry takes on importance for its applications in reactions of enantioselective or asymmetric synthesis of relevant compounds for Fine Chemistry, especially drugs. The results of the review carried out in the database of scientific literature, demonstrate the importance of the Crabtree's catalyst in hydrogenation and various asymmetric functional group transformation; also highlights the importance of the cycloocta-1,5-diene and tricyclohexylphosphine ligands, and a series of novel square-planar iridium(I) complexes analogous to Crabtree's catalyst, which have notorious catalytic applications. Since 1979, the number of citations has grown exponentially, not only in Organometallic Chemistry or Homogeneous Catalysis area, but also in areas such as Inorganic and Organic Synthesis, Industrial Chemistry, Nanotechnology or Green Chemistry. In the latter case, the Crabtree's catalyst has a special interest, considering that the "twelve principles" of Green Chemistry suggest expand the use of Catalysts, in order to obtain the benefits of the "Atom Economy" (minimize chemical waste or collateral reactions). The review indicates that there are numerous research possibilities with the Crabtree ' s catalyst and analogous compounds, and there are areas such as nanochemistry or bioorganometallic in which new applications can be studied.