Lithium is a very attractive material for batteries. It has low redox potential (-3.04V vs SHE) and high theoretical capacity of 3860 mAh g-1. So, lithium batteries would have high energy density. During charging and discharging of the batteries, the interface between electrode and electrolyte changes as lithium is deposited or dissolved. If the deposition is dendritic, it can short circuit and cause failure of the battery. During dissolution of lithium from the electrode, pits can form on the surface and some part of lithium is detached. It is called dead lithium since it is not electrochemically active. Solid electrolyte and lithium metal interfaces are characterized by high interfacial resistance. The interface between electrode and electrolyte is critical to the safety and performance of lithium batteries. The aim of this research is to understand the evolution of interface between electrode and electrolyte as charging or discharging occurs. Three kinds of interfaces are considered, interface formed between intercalation anode and liquid electrolyte, interface of metal anode and liquid electrolyte and interface between metal anode and solid electrolyte. Stringent performance and operational requirements in electric vehicles can push lithium-ion batteries toward unsafe conditions. Electroplating and possible dendritic growth are a cause for safety concern as well as performance deterioration in such intercalation chemistry-based energy storage systems. There is a need for better understanding of the morphology evolution due to electrodeposition of lithium on graphite anode surface, and the interplay between material properties and operating conditions. In this work, a mesoscale analysis of the underlying multi-modal interactions is presented to study the evolution of morphology due to lithium deposition on typical graphite electrode surfaces. It is found that electrodeposition is a complex interplay between the rate of reduction of Li ion and the intercalation of Li in the graphite anode. The morphology of the electrodeposited film changes from dendritic to mossy structures due to the surface diffusion of lithium on the electrodeposited film. Dendritic deposition on lithium metal anode during charging poses a safety concern. During discharging, formation of dead lithium results in low Coulombic efficiency. In this work, a comprehensive understanding of the interface evolution leading to the formation of dead lithium is presented based on a mechanism-driven probabilistic analysis. Non-dendritic interface morphology is obtained under reaction controlled scenarios. Otherwise, this may evolve into a mossy, dendritic, whisker or needle-like structures with the main characteristic being the propensity for undesirable vertical growth. During discharging, pitted interface may be formed along with bulk dissolution. Surface diffusion is a key determinant controlling the extent of dead lithium formation, including a higher probability of the same when the effect of surface diffusion is comparable to that of ionic diffusion in the electrolyte and interface reaction. One of the biggest advantages of solid electrolyte over liquid electrolyte is its mechanical rigidity which provides resistance to dendritic deposition. The electrodeposition at the interface of solid electrolyte and lithium metal anode will be affected by the nature of the interface formed between solid electrolyte and lithium metal, i.e. coherent, semi-coherent or incoherent depending on the misfit between the two crystal lattices. A coupled energetics and deposition mesoscale model is developed to investigate the nature of deposition and surface roughness of the deposition. The strength of interaction between metal anode surface and solid electrolyte surface at the interface is key in determining the roughness of the morphology during deposition. The energy is localized to region near the interface. With surface diffusion at the interface, the roughness of the interface as well as the energy near the interfacial region decreases.