Site-selective laser spectroscopy, Zeeman infrared and optical absorption have been employed to investigate trivalent dysprosium centers in rare-earth doped alkaline-earth fluoride crystals. These studies have characterised the two dominant centers in SrF₂:Dy³⁺ which are determined to be the fluorine compensated C₄ᵥ and C₃ᵥ centers analogous to those observed in other SrF₂:RE³⁺ systems. The C₃ᵥ center is shown to correspond to the J-center of Sr₁:Er³⁺, rather than the B-center reported for SrF₂:Ho³⁺. In CaF₂:Dy³⁺ three single Dy³⁺ ion centers have been characterised, corresponding to the C₄ᵥ , C₃ᵥ and cubic centers. Cluster centers involving more than one Dy³⁺ ion are also present in CaF₂:0.05%Dy³⁺, and such centers undergo efficient non-radiative cross-relaxation. This cross-relaxation eliminates the possibility of a direct investigation of the laser spectroscopy of these cluster centers, leading to the consideration of double doped systems. The laser spectroscopy of CaF₂:Dy³⁺:Eu³⁺ reveals a cluster center with efficient Dy³⁺→’Eu³⁺ energy transfer. Through a correlation of the Eu³⁺ fluorescence with previous studies of CaF₂:Eu³⁺ this center has been determined to be a heterogeneous R-center dimer. The double doped CaF₂:Dy³⁺:Gd³⁺ system has enabled the Dy³⁺ R-center fluorescence to be investigated. The polarised fluorescence of the C₄ᵥ centers in CaF₂:Dy³⁺ and SrF₂:Dy³⁺ has been analysed in terms of both electric dipole and magnetic dipole transition moments, from which it is shown that magnetic dipole processes are significant for Dy³⁺ fluorescence. The temperature dependence of fluorescence polarisation in praseodymium and europium doped CaF₂ and SrF₂ has been employed to investigate ionic motion in the C₄ᵥ centers. These experiments have enabled the barrier energies for interstitial reorientation to be determined in a site-selective manner. An anomalous temperature dependence of the polarisation anisotropy is observed in the Pr³⁺ C₄ᵥ centers, and has been shown to be a consequence of energy transfer between the C₄ᵥ centers.