Acceptor-doped barium zirconate is a promising proton-conducting oxide for various applications, for example, electrolysers, fuel cells or methane-conversion cells. Despite many experimental and theoretical investigations there is, however, only a limited understanding as to how to connect the complex microscopic proton motion and the macroscopic proton conductivity for the full range of acceptor levels, from diluted acceptors to concentrated solid solutions. Here we show that a combination of density functional theory calculations and kinetic Monte Carlo simulations enables this connection. At low concentrations, acceptors trap protons, which results in a decrease of the average proton mobility. With increasing concentration, however, acceptors form nanoscale percolation pathways with low proton migration energies, which leads to a strong increase of the proton mobility and conductivity. Comparing our simulated proton conductivities with experimental values for yttrium-doped barium zirconate yields excellent agreement. We then predict that ordered dopant structures would not only strongly enhance the proton conductivities, but would also enable one- or two-dimensional proton conduction in barium zirconate. Finally, we show how the properties of other dopants influence the proton conductivity.