We present first-principles electronic structure calculations of Mn-doped III–Vsemiconductors based on the local spin-density approximation (LSDA) as well as theself-interaction corrected local spin-density method (SIC-LSD). We find that it is crucial touse a self-interaction free approach to properly describe the electronic ground state. TheSIC-LSD calculations predict the proper electronic ground state configuration for Mn inGaAs, GaP, and GaN. Excellent quantitative agreement with experiment is found for themagnetic moment and p–d exchange in (GaMn)As. These results allow us to validatecommonly used models for magnetic semiconductors. Furthermore, we discuss the delicateproblem of extracting binding energies of localized levels from density functionaltheory calculations. We propose three approaches to take into account final stateeffects to estimate the binding energies of the Mn d levels in GaAs. We find goodagreement between computed values and estimates from photoemission experiments.