Persistent phosphors are increasingly investigated due to their potential applications in various fields, such as safety signage, dosimetry and in vivo imaging. These materials act as optical batteries that store and gradually release energy supplied during optical charging. As the energy is stored, or 'trapped', at specific defect sites in the host lattice, a clear understanding of the defects and trapping mechanisms in these materials is important for systematic improvement of their properties. Here, the thermoluminescence and afterglow properties of the near-infrared (NIR) emitting persistent phosphor LiGa5O8:Cr3+ (LGO:Cr) are studied. This phosphor is used as a model system for illustrating a more general approach to reliably derive trap depth distributions in persistent luminescent and storage materials. The combination of the Tstop-Tmax method with initial rise analysis is used to experimentally determine the presence of a broad distribution of trapping states. Computerized glow curve fitting is subsequently used to extract the relevant trapping parameters of the system in a rigorous, consistent manner, by fitting all the experimentally recorded data simultaneously. The resulting, single set of model parameters is able to describe all measured thermoluminescence and afterglow data and hence can be used to predict afterglow and storage properties of the phosphor under various conditions. The methods to analyze and describe the trap structure of the persistent phosphor LGO:Cr are straightforwardly applicable for other persistent and storage phosphors and result in a reliable determination of the relevant trapping parameters of a given material.