Negative bias temperature instability is regarded as one of the most important reliability concerns of highly scaled PMOS transistors. As a consequence of the continuous downscaling of semiconductor devices this issue has become even more important over the last couple of years due to the high electric fields in the oxide and the routine incorporation of nitrogen. During negative bias temperature stress a shift in important parameters of PMOS transistors, such as the threshold voltage, subthreshold slope, and mobility is observed. Modeling efforts date back to the reaction-diffusion model proposed by Jeppson and Svensson thirty years ago which has been continuously refined since then. Although the reaction-diffusion model is able to explain many experimentally observed characteristics, some microscopic details are still not well understood. Recently, various alternative explanations have been put forward, some of them extending, some of them contradicting the standard reaction-diffusion model. We review these explanations with a special focus on modeling issues.