Understanding the hydrated proton is a critically important problem that continues to engage the research efforts of chemists, physicists, and biologists because of its involvement in a wide array of phenomena. Only recently have several unique properties of the hydrated proton been unraveled through computer simulations. One such process is the detailed molecular mechanism by which protons hop between neighboring water molecules, thus giving rise to the anomalously high diffusion of protons relative to other simple cations. Termed Grotthuss shuttling, this process occurs over multiple time and length scales, presenting unique challenges for computer modeling and simulation. Because the hydrated proton is in reality a dynamical electronic charge defect that spans multiple water molecules, the simulation methodology must be able to dynamically readjust the chemical bonding topology. This reactive nature of the chemical process is automatically captured with ab initio molecular dynamics (AIMD) simulation methods, where the electronic degrees of freedom are treated explicitly. Unfortunately, these calculations can be prohibitively expensive for more complex proton solvation and transport phenomena in the condensed phase. These AIMD simulations remain extremely valuable, however, in validating empirical models, verifying results, and providing insight into molecular mechanisms.