Doping control is an important issue in wideband gap semiconductors such as nitrides and oxides that can be characterized by doping asymmetry, indicating that it is difficult to achieve both low-resistivity p- and n-type semiconductors. Despite theoretical predictions that group-V acceptors have high activation energies, p-type ZnO doped with N, P, As and Sb has been experimentally realized with a maximum hole concentration reaching 10(19) cm(-3). Recently, p-type conduction was also reported in ZnO doped with Li impurities. Based on the results of first-principles theoretical calculations,the electronic structure of various defects related to group-V and group-I dopants, the compensation mechanism of acceptors and the origin of p-type conduction in ZnO are discussed. Finally, control of p-type doping is examined with a focus on the activation of acceptors by co-doping with two different dopant sources and by hydrogenation followed by annealing.