The mechanisms of Diels-Alder reactions between 1,2,3-triazines and enamines have been explored with density functional theory computations. The focus of this work is on the origins of the different reactivities and mechanisms induced by substituents, and by hexafluoroisopropanol (HFIP) solvent. These inverse electron-demand Diels-Alder reactions of triazines have wide applications in bio-orthogonal chemistry and natural product synthesis. Both concerted and stepwise cycloadditions are predicted, depending on the nature of substituents and solvents. The nature of zwitterionic intermediates and the mechanism by which HET accelerates cycloadditions with enamines are characterized. Our results show the delicate nature of the concerted versus step wise mechanism of inverse electron-demand Diels-Alder reactions of 1,2,3-triazines, and that these mechanisms can be altered by electron-withdrawing substituents and hydrogen-bonding solvents.