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Ir-catalysis has been widely adopted in hydrogenation reactions for the transformation of unsaturated molecules to the corresponding saturated ones. We reviewed herein the DFT studies on mechanism of Ir-catalyzed homogeneous hydrogenations with respect to various hydrogen sources. Moreover, the stereochemistry and substituent effects in the Ir-catalyzed hydrogenations are considered. • Mechanistic studies towards Ir-mediated hydrogenation were summarized in this review. • General catalytic cycles given by theoretical studies are involved in each example. • Mechanism discussions are classified according to the substrates. • The understanding of mechanism would be helpful for further design new Ir-catalysis. Ir catalysis is widely used in hydrogenation reactions to transform unsaturated molecules to the corresponding saturated molecules. Understanding the reaction mechanism is helpful for design of new Ir-catalyzed hydrogenation reactions, as well as for controlling the regio/stereoselectivity. Density functional theory is a powerful tool for mechanistic study of organometallic catalysis, and it has been widely used to reveal the reaction pathways in this research area. With the development of computational methods, much progress has recently been made in mechanistic study of Ir-catalyzed hydrogenation reactions. Herein, we present a review of theoretical studies of the mechanism of Ir-catalyzed homogeneous hydrogenation. A redox pathway is commonly proposed for hydrogenation of non-polar unsaturated bonds, which involves oxidative addition of a hydrogen molecule to afford a high valence Ir hydride complex, insertion of an unsaturated bond into the Ir–H bond, and reductive elimination. Alternatively, the dihydrogen molecule can undergo a heterolysis reaction to provide a formal hydride ion and a proton. Subsequent nucleophilic and electrophilic attack can then also achieve hydrogenation of the polar unsaturated bond. In this review, the studies of the mechanism of Ir-catalyzed hydrogenation are classified according to the type of substrate: olefins, carbonyls, and imines. In each category, the reactions are discussed with respect to the various hydrogen sources. The stereochemistry and substituent effect in Ir-catalyzed hydrogenation are also considered. [ABSTRACT FROM AUTHOR]