TiO2 thin films grown on sapphire (alpha-Al2O3) ((1) over bar 10 (2) over bar) and on LaAlO3 (001) at 800degreesC by pulsed-laser deposition have been characterized by transmission electron microscopy. The TiO2 thin films grown on LaAlO3 (001) crystallize in anatase, while those on sapphire ((1) over bar 10 (2) over bar) crystallize in rutile. The epitaxial relationship between the anatase thin films and the LaAlO3 substrate is (004)[(1) over bar 10](A)//(001)[110](L), where the subscripts A and L indicate anatase and LaAlO3 respectively, and that between the rutile thin films and the sapphire substrate is (0 (1) over bar1)[(1) over bar 11](R)//[(1) over bar 10 (2) over bar)[20 (2) over bar(1) over bar](S), where the subscripts R and S indicate rutile and sapphire respectively. The rutile thin films contain a high density of growth twins with (101) and (0 (1) over bar1)(T) being the twin planes and [101] being the twinning direction, where the subscript T represents a twinning plane. The atomic structure of the twin boundary, the anatase-LaAlO3 and the rutile-sapphire interfaces were investigated by high-resolution transmission electron microscopy in combination with image simulations. Neither of the two epitaxial systems had a good lattice match between film and substrate. Growth mechanisms are discussed, on the basis of information on the atomic structure or the interfaces. Investigation also revealed that substantial similarity existed in the local atomic patterns of the substrate and the film for both systems, which is attributed to the formation of different TiO2 phases in different substrates.