A preeminent goal of organic synthesis is to achieve structural complexity with functional value in a step, atom, and time economical fashion. Cycloadditions, as exemplified by the Diels-Alder reaction, represent uniquely powerful processes to achieve this goal. Most of widely-used cycloadditions require transition metal or organic catalysts to achieve the desired control of reactivity and selectivity, which rely on mechanistic understandings at the molecular level. Modern density functional theory (DFT) calculations provide the foundation to achieve such level of understanding, and my PhD research focuses on studying the mechanism and selectivities of a series of important transition-metal-catalyzed and organocatalytic cycloadditions through DFT calculations. The first part of the thesis includes my studies on the mechanism and selectivities of transition-metal-catalyzed cycloadditions. Chapter 1 focuses on the mechanism and origins of selectivities in Ru(II)-catalyzed intramolecular (5+2) cycloadditions and ene reactions of vinylcyclopropanes and alkynes. The favored mechanism involves an initial ene-yne oxidative cyclization to form a ruthenacyclopentene intermediate, which is different from that found earlier with rhodium catalysts. Based on this new mechanism, solvent effect, chemoselectivity, diastereoselectivity and regioselectivity are explained. Chapter 2 includes the study of mechanism and ligand-controlled selectivities in [Ni(NHC)]-catalyzed intramolecular (5+2) cycloadditions and homo-ene reactions of vinylcyclopropanes and alkynes. The reaction mechanism of nickel catalysts is similar to that of ruthenium catalysts, which involves the alkyne-alkene cyclization to form a metallacyclopentene intermediate. The selectivity between the (5+2) and homo-ene products is determined in the subsequent competing reductive elimination and & beta;-hydride elimination steps. The anisotropic steric environments of SIPr and ItBu ligands are the major reasons for the reversed selectivity of these two similar-sized ligands. Chapter 3 emphasizes the study of terminal methyl effects in Rh(I)-catalyzed intermolecular (5+2) cycloadditions of vinylcyclopropanes and allenes. A competitive allene dimerization is found to irreversibly sequester the rhodium catalyst. This explains the necessity of methyl substituents on the reacting double bond of allenes to achieve the desired cycloadditions. The second part of the thesis focuses on my studies of the organocatalyzed cycloadditions. Chapter 4 illustrates the explorations of the mechanism and controlling factors of the organocatalyzed carbonyl-olefin metathesis. In the (3+2) cycloadditions between hydrazonium and alkenes, the distortion of reactants controls the reactivities. In the subsequent cycloreversions, the strain-release of the five-membered ring intermediates determines the reaction barriers. For these two reasons, the cyclopropene derivatives are found to be the most reactive in experiments. Chapter 5 discusses the distortion-acceleration effect of alkynyl substituents in the stepwise hexadehydro-Diels-Aleder (HDDA) Reaction. The HDDA reaction follows a stepwise mechanism with a diradical intermediate. The alkynyl substituent dramatically accelerates the HDDA reaction mainly by decreasing the distortion energy required to achieve the diradical transition state. Chapter 6 focuses on the mechanism and selectivity of N-triflylphosphoramide catalyzed (3+2) cycloaddition between hydrazones and alkenes. The protonation of hydrazones by Brønsted acid catalysts are found to be crucial for the facile (3+2) cycloaddition. This explains the acidity-dependent catalytic activities of this reaction. Based on the mechanism, we have also explained the origins of enantioselectivities when a chiral N-triflylphosphoramide catalyst is employed. Chapter 7 includes the study of mechanism and origins of switchable chemoselectivity of Ni-catalyzed C(aryl)-O and C(acyl)-O activation of aryl esters with phosphine ligands. For aryl esters, nickel with bidentate phosphine ligands cleaves C(acyl)-O and C(aryl)-O bonds via three-centered transition states, and this cleavage favors the weak C(acyl)-O bond. However, when monodentate phosphine ligands are used, the five-centered C(aryl)-O cleavage transition state makes C(aryl)-O activation favorable. In the case of aryl pivalates, nickel with bidentate phosphine ligands still favors the C(acyl)-O activation, but the subsequent decarbonylation requires very high barrier and the alternative C(aryl)-O activation occurs.