Rare earth ions embedded in crystals are natural high-quality-factor resonators that can be used for processing optically-carried broadband radio-frequency signals. This chapter focuses on the radio-frequency spectrum analysis function and describes different architectures that are designed to reach tens of gigahertz instantaneous bandwidth with submegahertz resolution. Various approaches are considered. The active material may act as a spectral buffer memory. Instead one may store a processing function inside the crystal. The latter may then operate either as a frequency-to-angle converter or a frequency-to-time transformer. All those architectures have been explored experimentally. To meet the specific requirements of these processors, frequency agile lasers have been developed. These keynote devices are described in detail.