Grain boundaries play a critical role in superconducting applications of Nb3Sn: in dc applications, grain boundaries preserve the material's inherently high critical current density by pinning flux, while in ac applications grain boundaries can provide weak points for flux entry leading to significant dissipation. We present the first ab initio study to investigate the physics of different grain boundary types in Nb3Sn and their impact on superconductivity using density-functional theory. We identify an energetically favorable selection of high-angle tilt and twist grain boundaries of distinct orientations. We find that clean grain boundaries free of point defects reduce the Fermi-level density of states by a factor of two, an effect that decays back to the bulk electronic structure ∼1-1.5 nm from the boundary. We further calculate the binding free-energies of tin substitutional defects to multiple boundaries, finding a strong electronic interaction that extends to a distance comparable to that of the reduction of density of states. Associated with this interaction, we discover a universal trend in defect electronic entropies near a boundary. We then probe the effects of defect segregation on grain boundary electronic structure and calculate the impact of substitutional impurities on the Fermi-level density of states in the vicinity of a grain boundary. We find that titanium and tantalum defects have little impact regardless of placement, whereas tin, copper, and niobium defects each have a significant impact but only on sites away from the boundary core. Finally, we introduce a model for a local superconducting transition temperature and consider how grain boundary composition affects Tc as a function of distance from the boundary plane. The methodology established in this manuscript can be applied to other A15 superconductors in addition to Nb3Sn. © 2020 IOP Publishing Ltd.