This thesis contains seven papers dealing with iridium and ruthenium based catalytic asymmetric reductions, either of ketones into chiral alcohols, or olefins into chiral alkanes. The first part of the thesis describes how we have designed and evaluated new bicyclic ligands containing either N,S or N,N chelating atoms. The ligands have been evaluated in the asymmetric Ir-catalyzed transfer hydrogenation of acetophenone. The complexes evaluated induced good enentioselectivity of the product. Moreover we have also utilized a commercially available chiral diamine (QCD-amine) as a ligand in the Ru-catalyzed hydrogenation of prochiral ketones, with excellent enantioselectivity for some of the substrates used. As part of this work we investigated, both theoretically and experimentally, the mechanism of this hydrogenation. Based on these results we have proposed a new reaction mechanism for this type of hydrogenations which involves active participation of the solvent in the catalytic cycle. The last part of the thesis describes the design, synthesis and evaluation of N,P and N₂C-carbene,N ligands for the Ir-catalyzed hydrogenation of carbon-carbon double bonds. The selectivities obtained in these investigations are among the best reported so far for a broad variation of substrates. A selectivity model for this hydrogenation has been derived and used in the rationalization of the results. As a part of this work we have synthesized and evaluated a new class of substrates, vinyl silanes, and showed that the scope of the hydrogenation reaction can be expanded to this new substrate class.