[en] Electron spin-resonance (ESR) spectra of Ce³⁺-doped LiCaAlF₆ (LiCAF) crystals measured at low temperature reveal three distinct Ce³⁺ centres in the crystal. The most intense spectrum is fitted to a spin Hamiltonian with trigonal symmetry and is associated with Ce³⁺ ions that substitute for Ca²⁺ ions in the LiCAF structure. Two other spectra have orthorhombic symmetry: they are assigned to Ce³⁺ ions with charge-compensating Li⁺-ion vacancies near to the Ce³⁺ impurity ions. The σ (E parallel a) and π (E parallel c) components of the polarized optical absorption and luminescence spectra of Ce³⁺ in LiCAF show there to be at least two Ce³⁺ centres. The intensities of optical transitions of Ce³⁺ are calculated using the eigenfunctions of the ground and excited states of Ce³⁺ in trigonal and orthorhombic symmetry and are compared with the observed polarizations of the absorption and luminescence. (author)