In various aspects, provided are solid oxide fuel cells with an operational temperature of less than about 500° C. that can provide, in various embodiments, a power density of greater than about 0.1 W/cm2 and/or have an ionic conductivity of greater than about 0.00001 ohm−1 cm−1. In various embodiments, provided are solid oxide fuel cells comprising a solid oxide electrolyte layer that is both an electronic and ionic conductor. In various aspects, provided are methods of making solid oxide fuel cells. In various aspects, provided are solid oxide materials comprising a polycrystalline ceramic layer less than about 100 nm thick having a ionic conductivity of greater than about 0.00001 ohm−1 cm−1 at a temperature less than about 500° C.