In materials with strong electron-phonon (e-ph) interactions, the electrons carry a phonon cloud during their motion, forming quasiparticles known as polarons. Charge transport and its temperature dependence in the polaron regime remain poorly understood. Here, we present first-principles calculations of charge transport in a prototypical material with large polarons, SrTiO_3. Using a cumulant diagram-resummation technique that can capture the strong e-ph interactions, our calculations can accurately predict the experimental electron mobility in SrTiO_3 between 150−300 K. They further reveal that for increasing temperature the charge transport mechanism transitions from band-like conduction, in which the scattering of renormalized quasiparticles is dominant, to an incoherent transport regime governed by dynamical interactions between the electrons and their phonon cloud. Our work reveals long-sought microscopic details of charge transport in SrTiO_3, and provides a broadly applicable method for predicting charge transport in materials with strong e-ph interactions and polarons
