Lithium-sulfur (Li-S) batteries are promising for electrical energy storage. Unlike intercalation compounds, the sulfur cathode undergoes a series of complex electrochemical reactions with substantial structural changes during charge and discharge. Various lithium polysulfides are formed that may shuttle between the electrodes, resulting in capacity loss and poor Coulombic efficiency. To identify the microscopic mechanisms, the structures and dynamics at the cathode/electrolyte interfaces in Li-S batteries were studied using first principles calculations. First, the equilibrium structures of various interfaces between α-sulfur and dimethoxyethane, which is a commonly used electrolyte, were determined. Then, the structural evolution was studied using ab initio molecular dynamics by adding lithium ions at a specific rate that simulates the discharge process. Based on these simulations, the elementary process that leads to the formation of soluable polysulfide was analyzed. Possible strategies that can be used for the rational design of the sulfur cathode with improved performance were proposed.