Co doped ZnO (Zn(1−x)Co(x)O) is studied as a prototype material for transition metal doped II–VI diluted magnetic semiconductors (DMSs) from first-principles and Monte Carlo simulations. The exchange interactions are calculated using the Korringa–Kohn–Rostoker (KKR) Green's function method. The exchange coupling constants thus obtained are treated in the classical Heisenberg model and the magnetic phase transitions are studied by the Monte Carlo technique. Our results show that the defect free substitutional DMSs of Zn(1−x)Co(x)O do not sustain magnetization at low concentration. At high concentration, we find layered magnetic structures. Ferromagnetism, with Curie temperature below room temperature, is stable at intermediate Co concentrations. First-principles studies with the generalized gradient approximation (GGA) and the GGA together with the Hubbard U are discussed with respect to structural and electronic properties of ZnO.