Abstract:The application and performance of conceptual and qualitative theories and quantitative quantum mechanical methods to the study of mechanism, reactivity, and selectivity of 1,3-dipolar and Diels-Alder cycloadditions are reviewed. This review emphasizes the application of conceptual density functional theory (DFT) for predicting reactivity and regioselectivity, and highly accurate quantum mechanical methods for predicting barrier heights and reaction energetics. Applications of computations to solvation effects, metal and organocatalysis, are also described.