Afterglow phosphors (or persistent luminescent materials) have the ability to emit light for a long time (up to hours) after the excitation has stopped. Currently, their main application is situated in emergency lighting and safety signage. In 1996, Matsuzawa et al. reported on the extremely long-lasting afterglow of SrAl2O4:Eu2+ co-doped with Dy3+ ions, which was more than 10-times brighter than the previously widely used ZnS:Cu,Co. Since then, research for stable and efficient persistent phosphors has continuously gained popularity. However, even today - almost 15 years after the discovery of SrAl2O4:Eu2+, Dy3+ - the number of persistent luminescent materials is still relatively low. Furthermore, the mechanism behind this phenomenon is still unclear. We present an overview of the important classes of known persistent luminescent materials and we take a closer look at the models and mechanisms that have been suggested to explain bright afterglow in various compounds. Also, methods for the evaluation of the brightness of afterglow phosphors are discussed, as the current standards do not take dark adaptation of the human eye into account. Finally, directions for phosphor development and future applications are given.