Dye-sensitized solar cells fabricated using ordered arrays of titania nanotubes (tube lengths 5, 10, and 20 mu m) grown on titanium have been characterized by a range of experimental methods. The collection efficiency for photoinjected electrons in the cells is close to 100% under short circuit conditions, even for a 20 mu m thick nanotube array. Transport, trapping, and back transfer of electrons in the nanotube cells have been studied in detail by a range of complementary experimental techniques. Analysis of the experimental results has shown that the electron diffusion length (which depends on the diffusion coefficient and lifetime of the photoinjected electrons) is of the order of 100 mu m in the titania nanotube cells. This is consistent with the observation that the collection efficiency for electrons is close to 100%, even for the thickest (20 mu m) nanotube films used in the study. The Study revealed a substantial discrepancy between the shapes of the electron trap distributions measured experimentally using charge extraction techniques and those inferred indirectly from transient current and voltage measurements. The discrepancy is resolved by introduction of a numerical factor to account for non-ideal thermodynamic behavior of free electrons in the nanostructured titania.