The characteristic optical spectra for shallow donors and acceptors in GaN are discussed. The most accurate photoluminescence (PL) data are obtained from samples grown on freestanding GaN substrates, where strain shifts are absent and a low spectroscopic line width is obtained. Recent PL data for excitons bound to the O and Si donors are discussed in some detail, giving accurate values for the binding energies and excited bound donor states. The Mg-acceptor is the most important one for p-doping, but the related optical spectra are controversial. We show that there are two acceptors present in Mg-doped GaN, with two different acceptor bound exciton peaks, and also two corresponding lower energy donor–acceptor pair spectra. We give tentative evidence for their interpretation.