Understanding interfacial phenomena such as ion and electron transport at dynamic interfaces is crucial for revolutionizing the development of materials and devices for energy-related applications. Moreover, advances in this field would enhance the progress of related electrochemical interfacial problems in biology, medicine, electronics, and photonics, among others. Although significant progress is taking place through in situ experimentation, modeling has emerged as the ideal complement to investigate details at the electronic and atomistic levels, which are more difficult or impossible to be captured with current experimental techniques. Among the most important interfacial phenomena, side reactions occurring at the surface of the negative electrodes of Li-ion batteries, due to the electrochemical instability of the electrolyte, result in the formation of a solid-electrolyte interphase layer (SEI). In this work, we briefly review the main mechanisms associated with SEI reduction reactions of aprotic organic solvents studied by quantum mechanical methods. We then report the results of a Kinetic Monte Carlo method to understand the initial stages of SEI growth.