The applications of aluminum compounds to homogeneous and heterogeneous catalyses are reviewed. This article starts with a brief overview of the synthesis, reactivity, and Lewis acidity of catalytically relevant aluminum alkyls, aluminum hydrides, and aluminum complexes, including insertion of small molecules into Al–H and Al–C bonds. The following section focuses on alkylaluminoxanes with emphasis on the synthesis, structure, and reactivity of methylaluminoxane (MAO) and modified methylaluminoxanes (MMAO). Polymerization and oligomerization of alkenes are the subjects of the next section. Coverage includes the use of organoaluminum activators, such as triethylaluminum, MAO, and MMAO, for large-scale transition metal-catalyzed reactions including Ziegler–Natta and single-site metallocene-catalyzed polymerization of alkenes and selective alkene dimerization and trimerization processes. Also discussed are aluminum-catalyzed oligomerization of ethylene to long-chain terminal alkenes, polymerization of ethylene by cationic aluminum complexes, and the Lewis pair polymerization of conjugated polar alkenes catalyzed by frustrated Lewis pairs of aluminum. The ring-opening polymerization of epoxides, lactides, and lactones is then reviewed. Proposed monometallic and bimetallic mechanisms are discussed. This section also includes the aluminum-catalyzed copolymerization of epoxides with carbon dioxide to give polycarbonates and conversion of epoxides to cyclic carbonates. The next-to-last section of this article overviews the roles of aluminum in heterogeneous catalysis, and includes acid-catalyzed reactions on alumina, zeolites, and aluminophosphates. Transition metal catalysts supported on alumina are also discussed, both those where the transition metal is the active catalyst and bifunctional catalysts where both the alumina support and the transition metal contribute to the catalytic activity. This includes a brief discussion of large-scale commercial processes such as methanol to olefins technology and the hydrodesulfurization, hydrodenitrogenation, catalytic cracking, and reforming of petroleum. The final section briefly provides a few examples of the applications of aluminum catalysts to organic synthesis and fine chemicals production. Readers are referred to leading works that more adequately describe the extensive use of homogeneous and heterogeneous aluminum catalysts in these areas. One hundred four reviews and original works are cited.