This chapter provides a theoretical exploration of the spectral intensities of rare-earth ionsRare-earth ions in vitreous hosts, focusing on the Judd–Ofelt theoryJudd–Ofelt theory. It addresses the fundamental problem of parity-forbidden 4f → 4f transitions, explaining how this theoretical model allows these transitions through the mixing of electronic states with opposite parity induced by the local crystal field. The methodology for applying this semi-empirical theory is detailed, demonstrating how the three intensity parameters (Ω2, Ω4, and Ω6) are derived from experimental absorption spectra by calculating oscillator strengthsOscillator strengths. These parameters are then used to predict essential radiative properties such as transition probabilities and lifetimes. Beyond the standard Judd–Ofelt framework, the chapter delves into the origins of hypersensitive transitions, introducing the covalency modelCovalency model and the nephelauxetic effect to explain the strong influence of the local ligand environment on spectral intensities. The role of crystal-field theoryCrystal-field theory and dynamic coupling mechanisms in providing a more complete description of the rare-earth ions’Rare-earth ions local environment and transition dynamics is also discussed, offering a comprehensive theoretical toolkit for the structural and spectroscopic analysis of materials doped with rare-earth ionsRare-earth ions.