Aquaporins and aquaglyceroporins are passive membrane channels that, in many species, facilitate highly efficient yet strictly selective permeation of water and small solutes across lipid bilayers. Their ability to block proton flux is particularly remarkable, because other aqueous pores and water efficiently conduct protons, via the so-called Grotthuss mechanism. How efficient water permeation is achieved and how it is reconciled with the seemingly contradictory task of strict proton exclusion have been long-standing puzzles. Because neither the dynamics of the water molecules nor the mobility of protons inside the aquaporin channel could be experimentally accessed so far, several groups addressed this challenge using a variety of atomistic computer simulation methods.