This article outlines the main results of a research and development cooperation between Philips Research Eindhoven; Peter the Great St. Petersburg Polytechnic University; Ioffe Institute, St. Petersburg; Utrecht University; and Philips Healthcare. It reviews the properties of garnet ceramics in the (Lu,Gd)3(Ga,Al)5O12:Ce system for medical imaging, especially time-of-flight positron emission tomography (PET). Thermally stimulated luminescence (TSL) peaks are attributed to impurities, verified by intentional codoping of samples. A lately developed method allows extraction of carrier lifetimes, thermal trap depths, and frequency factors from TSL and afterglow measurements. A detailed analysis reveals the presence of a distribution of trap depths, allowing a more accurate afterglow modeling. Activation energies of thermal ionization and trap depths obtained from TSL show the influence of Ga/Al substitution on thermal quenching and on trap position. The resulting nonmonotonic dependence of the conduction band edge with Ga content in (Lu,Gd) garnets is consistent with earlier predictions. Shallow traps determine both signal decay and short-term afterglow. The impact of signal height, rise, and decay times on coincidence resolving time and further on PET image quality is described by analytical models.