Methods of synthesis of nanotubular structures based on titania of various phase and chemical compositions are described. A systematic account is given of known data about the influence of synthesis and subsequent treatment conditions on the amorphous and crystal structures, specific surface area, morphology and optical, luminescence and electro-physical properties of titania-based nanotubular oxide materials. The photocatalytic properties in the oxidation reactions of organic compounds and the performance characteristics of the memristive behaviour of TiO2-based nanotubular structures are considered in details. Their applications are discussed.The bibliography includes 238 references.

The catalytic activity of nanotubular titanium dioxide films formed during the oxidation of acetone to carbon dioxide under the action of visible light with a wavelength of 450 nm was found to be approximately 2 times higher compared to standard titanium dioxide (Degussa P25). The nanotubular films were grown by the anodization of titanium foil using an original technique. Diffuse reflectance spectra of the films are attributed to enhanced activity in the visible spectrum by the nonstoichiometry of titanium dioxide near the interface between the nanotubular film and the titanium foil substrate.

The local atomic environment of lattice vacancies in titanium monoxide has been specifically studied by positron annihilation techniques in the composition range from ${\mathrm{TiO}}_{0.74}$ to ${\mathrm{TiO}}_{1.26}$. For nonstoichiometric titanium monoxide, a high concentration of vacancies has been suggested on both the titanium and the oxygen sublattice. From the analysis of the core electron momentum distribution of the atoms surrounding the vacancies in disordered as well as in ordered titanium monoxide, oxygen atoms are identified to form the local vacancy environment, indicating that positrons are trapped by titanium and not by oxygen vacancies. Positron lifetime measurements have shown that the decrease of the oxygen content, $y$, and the process of disordering in nonstoichiometric titanium monoxide ${\mathrm{TiO}}_y$, are accompanied by an increase of the valence electron density on the titanium vacancy.

Conductivity and magnetic susceptibility of disordered cubic titanium monoxide TiOy(0.920≤ y≤1.262) are studied. Temperature dependences of the conductivity of TiOy monoxides with y≤1.069 are...