The structures, energetic, and vibrational properties of MDyX4 (M = Li, Na, K, Rb, Cs; X = F, Cl, Br, I) mixed alkali halide/dysprosium halide complexes have been investigated by a joint computational and experimental, matrix-isolation Fourier-transform infrared spectroscopic (MI-IR), study. According to our DFT computations for the complexes with heavier halides and alkali metals the ground-state structure is the tridentate isomer; while at high temperatures the bidentate structural isomer dominates. The survey of various dissociation processes revealed the preference of the dissociation to neutral MX and DyX3 fragments over ionic and radical dissociation products. Cationic complexes are considerably less stable at 1000 K than the neutral complexes, and they prefer to dissociate to M+ DyX4 degrees fragments. The vapor species of selected mixtures of NaBr and Cs Br with DyBr3 and of CsI with DyI3 in the temperature range 900-1000 K have been isolated in krypton and xenon matrices and investigated by infrared spectroscopy. Besides the characteristic vibrational frequencies of the monomeric and dimeric alkali halide species and of the dysprosium trihalide molecules, certain signals indicated the formation of MDyX4 (M = Na, Cs; X = Br, I) mixed complexes. Comparison with the computed vibrational and thermodynamic characteristics of the relevant species lead to the conclusion that these complexes appear in the vapor predominantly as the C-2v-symmetry bidentate isomer. This is the first time that this structure was identified in an experimental vibrational spectroscopic study. The signals appearing upon performing a thermal anneal cycle were tentatively assigned to the double complex M(2)yX(5) (M = Na, Cs; X = Br, I). A structure in which one alkali atom is bound to dysprosium by three and the other by two bridges is proposed for these double complexes.