Materials of the La2/3-xLi3xTiO3–family have been studied by selected area electron diffraction (SAED), high-resolution transmission electron microscopy (HRTEM), powder synchrotron X-ray diffraction and powder neutron diffraction. HRTEM showed that the materials have a complex domain-microstructure. The size and shape of the domains have been obtained from synchrotron X-ray diffraction data; besides, other extended defects such as strains and compositional fluctuations have been detected. The complementary use of local (SAED and HRTEM) and average (SXRD and NPD) techniques have allowed us to propose a model to refine the crystal structure of these oxides also accounting for their microstructure. All these materials have a perovskite-related structure with a diagonal unit cell (≈√2ap x √2ap x 2ap) as a consequence of the tilting of the TiO6 octahedra. Ordering of lanthanum and lithium ions and vacancies along the 2ap-axis, as well as displacements of titanium ions from the centre of the octahedra, have been determined. The Li+ ions present a distorted square planar coordination and are located in interstitial positions of the structure, which could explain the very high ionic conductivity of this type of materials. The lithium conductivity depends on the oxide composition and its crystal microstructure, which varies with the thermal treatment of the sample.