 Persistent luminescence materials have been studied extensively since the 1970s, with most research focusing on EU2 plus doped compounds. However, recent years have seen a steady increase in the number of papers published on non-EU2 plus-based materials, with over 80% of them being based on intrinsic host defects, transition metals, or trivalent rare earths. This review provides an overview of these materials and their afterglow properties, as well as the remaining challenges, including excitability with visible light and energy transfer between multiple luminescent centers. The paper concludes by outlining the necessary elements for a complete description of a persistent luminescent material, allowing for a more objective comparison of these phosphors.