Understanding acceptors has been one of the most important issues in the development of the nitride semiconductors. Acceptor impurities are crucial to establishing p-type doping, and acceptor-type defects may act as sources of luminescence or as carrier traps. In this Special Issue, Lyons et al. (pp. 900–908) review recent theoretical studies of acceptor dopants, defects, and impurities in the nitride semiconductors. Advanced first-principles calculations are now capable of quantitatively predicting acceptor properties, and recent studies have shed light on the limits of conductivity in p-type material, as well as the role of unintentional impurities such as carbon. Also presented here are new results on gallium vacancies and their complexes with donors. These acceptors are thought to be the dominant point defects in GaN, and have often been linked to deep-level luminescence. As shown in the cover figure, the authors have used first-principles techniques to calculate the luminescence signals caused by a range of vacancy complexes. [To honour the laureates of the Nobel Prize in Physics 2014, the cover of this pss (b) issue shows a specially designed pss logo assembled from blue nitride LEDs (courtesy of Armin Dadgar, Technical University of Magdeburg)].