Using hybrid functional theory together with experimental measurements, we investigate the influence of gallium impurities and their complexes on electrical properties of ZnO. In contrast to the behavior of isolated Ga impurities and native defects, the calculated formation energies of Ga complexes are consistent with our experimental data. We show that for high levels of Ga doping the acceptor behavior of Ga Zn-V Zn and Ga Zn-O i complexes explains the conductivity measurements and compensation levels in ZnO. The computed binding energies of these complexes are also consistent with the binding energies obtained from the measurements of the temperature dependence of carrier mobility. Our results show that the formation of defect complexes, often overlooked by theory, can be indispensable in capturing the defect physics.