In this thesis, DFT method together with thermodynamic and kinetic approaches has been applied to study the following properties and processes of electrode materials: i) insertion and transport of Li ion in TiO2-B, ii) formation and migration of charge carriers in LiX (X = I, Br, and Cl), iii)intercalation of AlCl4 into graphite, and iv) effect of dopant on the properties of LiNiO2. Our studies on the first and second systems show that, depending on the type of materials, kinetic or thermodynamic factor plays key role in determining the specific capacity and ionic conductivity. By calculating the diffusion length of Li as a function of C-rate, we find that the energy barrier of Li transport controls the size-sensitivity of capacity in TiO2-B, which is widely studied as anode in Li-ion battery. However, the calculated activation energies of Li ion in LiX, which can be components of solid electrolyte interphase layer in Li-ion battery, show that the ionic conductivity is determined by the defect formation energy (concentration) and not by diffusion barrier. A comparison between our simulated XRD pattern and experimental ones from our collaborator for a novel Al-ion battery shows that reversible insertion of AlCl4 into graphite cathode occurs via staging mechanism from stage 6 to stage 3 during the charge process. Our combined theoretical-experimental study for Zr doping of LiNiO2, which is a promising cathode of next generation Li-ion battery shows that low-level doping will promote the cation mixing in LiNiO2 but not change the Li vacancy formation energy.