Abstract: Chapter 1 evaluates the abilities of the B3LYP, MPW1K and BPW91 density functional methods and HF theory to reproduce well-known substituent effects in Diels-Alder cycloadditions of cyclopentadiene and 9,10-dimethylanthracene with ethylene and the series of cyanoethylenes. Whereas HF and MPW1K accurately reproduces substituent effects in reactions involving tri- and tetra-substituted ethylenes, significant errors are found with the popular B3LYP method. In Chapter 2, substituent effects in Diels-Alder cycloadditions of symmetrical dienes and nucleophilic dienes with ester-substituted alkenes and alkynes are evaluated with B3LYP, MPW1K and HF methods. Alkynes are usually as reactive as alkenes in cycloadditions involving symmetrical dienes but are markedly more reactive in cycloadditions involving nucleophilic dienes. These reactivities are explained by the structural features of the transition state geometries. These findings rationalize experimentally observed regioselectivities and chemoselectivities in Diels-Alder cycloadditions of dienes with enyne dienophiles. Chapter 3 rationalizes the surprising activation of alkenes substituted by α-ethynyl groups by the ability of α-ethynyl substituents to stabilize the developing negative charge in the transition structures of reactions. These substituents cause repulsive interactions in endo-TSs leading to high exo-ethynyl selectivities. Computational investigations on possible rearrangement mechanisms for the assembly of the pyrimidinone core of an anti-HIV drug, raltegravir, are described in Chapter 4. The results suggest that a novel polar radical-pair mechanism is favored over mechanisms involving [1,3] or [3,3]-shifts, in support of experimental evidence. Substituent effects in 1,3-dipolar cycloadditions of azides with alkenes and alkynes are explored with the high-accuracy CBS-QB3 method in Chapter 5. These studies evaluated the possibilities for noncatalytic activation and reversibility or irreversibility in these reactions and explored the likelihood of their use in Dynamic Combinatorial Chemistry (DCC) or Click chemistry. Chapter 6 describes computational investigations on aza-Cope rearrangements of cationic enammonium reactants in water and a supramolecular assembly which had been studied experimentally by Bergman and coworkers. The MPW1K method performs better than B3LYP method for these rearrangements. The results suggest that the reactants rearrange via low-energy chair TSs, but these have high-energy 'boat-like' geometries in the host which raise the energy of the reactants near the TS leading to catalysis.