Alkali metal-sulfur cells and batteries with cathode layers that store alkali metal charge carriers (e.g., lithium ions) in agglomerates of sulfurized carbon. The cathode layers lack costly and environmentally unfriendly nickel and cobalt. The cathode layers are composites that include agglomerates of sulfurized-carbon particles in a conductive binder and interconnected by sp2-bonded carbon materials, such as carbon nanotubes or nanoribbons, that extend within the agglomerates and between the sulfurized-carbon particles.