Intermediate and final discharge products of the lithiation of sulfur in C-S cathodes of Li-S batteries are extremely dependent on cathode morphology. When the cathode is a composite of carbon and sulfur, such morphology is in turn a function of the synthesis method. In spite of these complexities, some basic ideas can be formulated to prepare a model able to describe the C-S cathode characteristics and evolution. Here we use classical molecular dynamics with a reactive force-field to evaluate the cathode morphology and its evolution during lithiation in contact with a liquid (with or without S-containing additives) or with a solid electrolyte. The interfacial chemistry is examined with density functional theory and ab initio molecular dynamics. The same methods are used to o study the electronic conductivity of the potential insoluble products.