Acceptor defects and impurities play a critical role in the performance of GaN-based devices. Mg is the only acceptor impurity that gives rise to p-type conductivity, while other acceptors (such as C N impurities and V Ga defects) act as sources of compensation and trapping. From the point of view of theory, understanding the physics of acceptor species in GaN has long been a challenge. In the past, limitations of computational techniques made it difficult to quantitatively predict crucial quantities such as thermodynamic and optical transition levels. However, advances in first-principles calculations, including the use of hybrid functionals in density functional theory, have led to a resurgence in efforts to understand properties of acceptors in nitrides. After briefly discussing advances in theoretical techniques, we review recent computational work on acceptor impurities in GaN and compare theoretical results with the available experimental data. We also present new hybrid density functional calculations on the transition levels of V Ga and its complexes with O and H impurities. The results indicate that donor impurities significantly lower V Ga transition levels, and that V Ga -3H and V Ga -O N -2H complexes give rise to yellow luminescence. We also discuss the properties of acceptor impurities in AlN and InN.