The structure and ionic conductivity of orthorhombic beta-YF3 structured rare earth fluorides and of tysonite-structured ones are investigated. Temperature dependencies of the conductivity of various orthorhombic crystals are close to one another. The conductivity at 500 K, 9500, and the conduction activation enthalpy, DeltaH, are equal to 1.1(4) x 10(-5) S/cm and 0.70(3) eV, respectively. The conductivity of tysonite-structured crystals is significantly higher (sigma(500)=(1.4(8)) x 10(-3) S/cm, DeltaH = 0.36(1) eV), and can be further enhanced by doping with alkaline-earth fluorides. The highest conductivity is found for LaF3:5 m/o SrF2 (sigma(500) = 2.4 x 10(-2) S/cm, DeltaH=0.35(1) eV). In both structural types, the conductivity is isotropic. A significant difference between the conductivities of both structural types of rare earth fluorides is discussed.