Density functional theory electronic structure calculations were used to explore the mechanism for the Diels-Alder reaction between 2,5-dimethylfuran and maleic anhydride (MA). Reaction paths are reported for uncatalyzed and Lewis and Bronsted acid-catalyzed reactions in vacuum and in a broad range of solvents. The calculations show that, while the uncatalyzed Diels-Alder reaction is thermally feasible in vacuum, a Lewis acid (modeled as Na+) lowers the activation barrier by interacting with the dienophile (MA) and decreasing the HOMO-LUMO gap of the reactants. A Bronsted acid (modeled as a proton) can bind to a carbonyl oxygen in MA, changing the reaction mechanism from concerted to stepwise and eliminating the activation barrier. Solvation effects were studied with the SMD model. Electrostatic effects play the largest role in determining the solvation energy of the transition state, which tracks the net dipole moment at the transition state. For the uncatalyzed reaction, the dipole moment is largely determined by charge transfer between the reactants, but in the reactions with ionic catalysts, there is no simple relationship between solvation of the transition state and charge transfer between the reactants. Nonelectrostatic contributions to solvation of the reactants and transition state also make significant contributions to the activation energy.