Solid oxide fuel cells (SOFCs) are efficient electrochemical devices that allow for the direct conversion of fuels (their chemical energy) into electricity. Although conventional SOFCs based on YSZ electrolytes are widely used from laboratory to commercial scales, the development of alternative ion-conducting electrolytes is of great importance for improving SOFC performance at reduced operation temperatures. The review summarizes the basic information on two representative families of oxygen-conducting electrolytes: doped lanthanum aluminates (LaAlO3) and lanthanum gallates (LaGaO3). Their preparation features, chemical stability, thermal behaviour and transport properties are thoroughly analyzed in terms of their connection with the target functional parameters of related SOFCs. The data presented here will serve as a starting point for further studies of La-based perovskites, including in the fields of solid state ionics, electrochemistry and applied energy.