The peak manifestation of nonstoichiometry in fluoride systems in the number of phases with valuable properties and wide homogeneity ranges is 45 MF2-RF3 systems, where M = Ca, Sr, Ba and R are 15 rare earth elements from La to Lu and Y (with Pm and Sc excluded). A deviation from stoichiometry in crystals of the M 1 − x R x F2 + x (CaF2 fluorite type) and R 1 − y M y F3 − y (LaF3 tysonite type) phases is responsible for the fluorine superionic conductivity σ. The range of variation in σ with changes in the qualitative (M, R) and quantitative (x, y) compositions in both structure types is very wide. The σ value changes by a factor of 108 in the M 1 − x R x F2 + x phases (at 500 K) and by a factor of 106 in the R 1 − y M y F3 − y phases (at 293 K). Changing compositions, one can also obtain crystals with σ values large enough for their use as fluorine-conducting solid electrolytes. Phases promising for solid electrolytes were revealed in the MF m -RF n systems (m < n ≤ 4), which were studied within the program of searching for new multicomponent fluoride materials at the Institute of Crystallography, Russian Academy of Sciences (IC RAS). Superionic conductivity is one of the peak manifestations of the influence of defect structure of nonstoichiometric crystals on their properties. The subject of this review is the results of the studies performed at the IC RAS on the ionic conductivity of single crystals of the M 1 − x R x F2 + x and R 1 − y M y F3 − y nonstoichiometric phases.