Silicon (Si) has been considered as a promising negative electrode material for lithium ion batteries (LIBs) because of its high theoretical capacity, low discharge voltage, and low cost. However, the utilization of Si electrode has been hampered by problems such as slow ionic transport, large stress/strain generation, and unstable solid electrolyte interphase (SEI). These problems severely influence the performance and cycle life of Si electrodes. In general, ionic conduction determines the rate performance of the electrode, while electron leakage through the SEI causes electrolyte decomposition and, thus, causes capacity loss. The goal of this thesis research is to design Si electrodes with high current efficiency and durability through a fundamental understanding of the ionic and electronic conduction in Si and its SEI. Multi-scale physical and chemical processes occur in the electrode during charging and discharging. This thesis, thus, focuses on multi-scale modeling, including developing new methods, to help understand these coupled physical and chemical processes. For example, we developed a new method based on ab initio molecular dynamics to study the effects of stress/strain on Li ion transport in amorphous lithiated Si electrodes. This method not only quantitatively shows the effect of stress on ionic transport in amorphous materials, but also uncovers the underlying atomistic mechanisms. However, the origin of ionic conduction in the inorganic components in SEI is different from that in the amorphous Si electrode. To tackle this problem, we developed a model by separating the problem into two scales: 1) atomistic scale: defect physics and transport in individual SEI components with consideration of the environment, e.g., LiF in equilibrium with Si electrode; 2) mesoscopic scale: defect distribution near the heterogeneous interface based on a space charge model. In addition, to help design better artificial SEI, we further demonstrated a theoretical design of multicomponent SEIs by utilizing the synergetic effect found in the natural SEI. We show that the electrical conduction can be optimized by varying the grain size and volume fraction of two phases in the artificial multicomponent SEI.