Lithium-sulfur batteries are sought as promising candidates for electric vehicle technologies. The soluble polysulfide (PS) migration from cathode to anode and their posterior decomposition at the Li-metal anode side, and the low electronic conductivity of the main discharge products Li₂S₂ and Li₂S are among the main challenges. Here we use a multiscale modeling approach to evaluate and characterize these issues. Reactivity of the electrolyte at the bulk and at the anode surface and the transport mechanisms of the soluble polysulfides are studied with density functional theory and ab initio molecular dynamics. The composite carbon-sulfur cathode is modeled at the atomistic and mesoscopic levels and the effects of changes of morphology during reaction are investigated through the analysis of battery performance. The carbon-sulfur composite properties are compared to those resulting of a novel pressurized autogenic synthesis route. Finally, the important effects of precipitation modes and low electronic conductivity of the insoluble Li₂S₂ and Li₂S species on charge reactions and cathode capacity are also evaluated with a multiscale modeling approach.