Abstract: Cycloaddition reactions in general represent one of the most powerful strategies for the synthesis of cyclic compounds. The Diels-Alder (DA) and 1,3-dipolar cycloaddition (13DC) reactions are the most common types of cycloaddition reaction which lead to the formation of six- and five-membered rings, respectively. In our continuing efforts to contribute to the understanding of DA and 13DC reactions; we studied the following theoretically:1. The 13DC reactions of the pyridinium-3-olates and pyrazinium-3-olates with methyl acrylate and methyl methacrylate [1-5].2. The competitive hetero-DA and 13DC reactions of methyl glyoxylate oxime and its tautomeric nitrone with cyclopentadiene in the absence and in the presence of BF3 as a Lewis acid catalyst [6].3. The 13DC reactions of C60 with substituted nitrile oxides (RCNO; R = F, Cl, Br, NC, CN and NO2) [7].Among the outcomes of our investigations is the successful use of theoretical methods to understand the regio- and stereoselectivity of the reactions considered. It is expected that experimentalists will find the results useful for synthesis involving these moieties.