Nanostructured materials are featured by providing a variety of favourable electrical properties, as the reduced ion and electron transport paths enable significant enhancement on (de)intercalation rates and hence high power. For TiO2 anatase, nano-sizing results in a curved open cell voltage profile with a much shorter plateau region in comparison with that of micron sized materials. The main objective of this thesis is to gain insight in the impact of particle size on the Li-ion storage and Na-ion storage in anatase TiO2 using a combined experimental, theoretical approach. In addition a novel Na-ion titanium oxide storage compound is tested and characterized. Nanostructuring has a striking influence on the thermodynamics and kinetics of Li-ion insertion reactions in anatase TiO2. The particle size dependent phase transformations in anatase TiO2 upon lithiation are systematically studied. The equilibrium voltage measured by galvanostatic intermittent titration technique decreases progressively with particle size reduction, which is attributed to the difference in surface energy of the pristine and lithiated phases. Based on the evolution of domain size and phase fraction of the two phases, it is concluded that the first-order phase transition proceeds by continuous nucleation upon lithium insertion. For all particle sizes the phase boundary is found to migrate under non-equilibrium conditions even under very slow (dis)charge conditions. Remarkably, the degree of non-equilibrium condition increases with particle size decreasing, which is rationalized by the difference in the observed phase transition behaviour between small and large particles. The absence of phase coexistence in smaller particles in combination with the sluggish ionic transport rationalizes the better electrochemical performance of the nano-structured anatase TiO2 as compared to the micro sized material. These results suggest a very low nucleation barrier for the formation of new phases and a sluggish ionic migration during phase boundary movement. Therefore strategies to improve the rate performance of nano structured anatase TiO2 should concentrate on improving the interstitial diffusion, for instance by appropriate doping with Nb or Zn. Based on the experimental study on the particle size dependent phase transition behaviour, the impact of particle size and surface orientation on the lithium ion insertion in anatase TiO2 is systematically investigated by using DFT first-principles calculations and surface cluster expansion. Nano-sized TiO2 is modelled by surface slabs with two thermodynamically stable orientations {101} and {001}. The calculated formation energies for bulk and surface structures suggest that the stable Li configuration of Li0.5TiO2 titanate phase depends on the surface orientation. For the Li composition below Li0.5TiO2, the calculated size dependent voltage curves are in qualitative agreement with the experimental results. The calculations show that the voltage difference between the different surface orientations is due to the different Li-O and Ti-O bond length in the surface region. For the Li composition above Li0.5TiO2, the relative magnitudes of the voltage profiles between different surface directions and particle sizes are not consistent with the experimental observations. This is suggested to be the consequence of the stoichiometric surface slabs. A surface excess of oxygen is shown to explain the larger intercalation voltages in smaller particles with the composition above Li0.5TiO2. The demand for renewable energy resources has initiated the search for high performance and cost effective battery systems. Na-ion as a charge carrier is one of the most promising alternatives to Li-ions due to its high abundance, low cost, and comparable high cell potential. Rudola et al. explored Na-ion storage in a novel compound Na2Ti6O13, demonstrating a reversibly uptake of 1 Na ion per formula unit (49.5 mAh/g) by a solid solution mechanism at an average potential of 0.8 V In this thesis it is shown that by lowering the cut-off voltage from 0.3 V to 0 V vs Na/Na+ the capacity of the layered Na2Ti6O13 negative electrode material can be enhanced from 49.5 mAh/g (Na2+1Ti6O13) to a promising 196 mAh/g (Na2+4Ti6O13) for at least 10 cycles, after which it gradually reduces. To understand the structural changes in-situ X-ray diffraction is performed and compared with Density Functional Theory calculations. A consistent evolution of the lattice parameters and Na-ion positions is observed. The results show that Na-ion intercalation in the Na2+xTi6O13 host structure is limited to Na2+2Ti6O13 in a solid solution reaction. Only small changes in lattice parameters indicate that the insertion reaction is highly reversible. Further increasing the Na composition below 0.3 V appears to lead to loss in crystallinity, which in combination with solid electrolyte interface formation is suggested to be the origin of the gradually reducing reversible capacity. The promising Li-ion storage properties of TiO2 anatase provide the motivation to embark on the study of Na-ion insertion in anatase TiO2. Electrochemical and X-ray experiments and DFT calculations are performed to improve the understanding about the particle size dependent electrochemical Na-ion storage in the TiO2 anatase. Reducing the particle size results in a distinct increase of the reversible capacity, also introducing stronger degradation of the cycling stability. The highest specific reversible capacity (210mAh/g) was found for 7 nm TiO2 anatase, which is among the largest reported in literature. Although bulk storage is generally assumed, X-ray diffraction on the electrodes after discharge and charge shows negligible changes on the lattice parameters, indicating that Na-ion insertion in the TiO2 lattice does not occur significantly. Nevertheless DFT calculation predicts that the fully occupied Na1TiO2 (capacity 334mAh/g) can be thermodynamically achieved at a positive voltage (0.3V). The fact that Na-ion insertion does not occur is most likely due to the large energy barrier for Na-ion diffusion which is calculated to be ~0.84eV at the dilute limit. These results indicate that the inserted sodium ions are mainly accommodated at the surface region. Therefore strategies to improve the electrochemical performance of Na storage by TiO2 anatase should focus on improving the surface and electrolyte stability.