Titanium dioxide (TiO2) has been proposed as a potential electrode material for lithium, sodium, and magnesium ion batteries. Among the phases of TiO2, anatase, rutile, and (B) TiO2 are the most commonly used phases for electrochemical storage, while the amorphous phase has also been shown to be a promising candidate. We present a comparative density functional theory study of the insertion energetics of Li, Na, and Mg into anatase, rutile, and (B) TiO2, as well as into the amorphous phase. Our results show that among the crystalline phases, (B) TiO2 provides the strongest binding between TiO2 and the inserted Li/Na/Mg atom. We also find that for all Li, Na, and Mg, the amorphous phase provides insertion sites well-dispersed in energies, with a lowest energy site more thermodynamically favorable than insertion sites in the crystalline phases. We also obtain the localized Ti3+ states together with the formation of the defect states in the band gap, which are induced by the insertion, at the GGA level of theory (without the Hubbard correction). (C) 2014 Elsevier B.V. All rights reserved.