Lithium-sulfur (Li-S) batteries are postulated as alternatives to existing Li-ion battery technology; however, their practical use is often hampered by the polysulfide shuttle. Here, we report on the synthesis of sulfurized poly(styrene) (SPS) and sulfurized poly(vinylpyridine) (SPVP) as cathode materials for Li-S batteries. A simple and scalable synthetic method offers access to sulfurized polymers with ≥60 wt.% sulfur, in which all the sulfur is covalently bound to the polymer. Together with the sulfur covalently bound to the polymer, the nanostructured morphology, uniform sulfur distribution, and porous structure synergistically allow for a capacity of 1250 and 1400 mAh g-1 for SPS and SPVP, respectively, with >70% capacity retention after 700 cycles at C/2-rate with >98% coulombic efficiency. Such excellent electrochemical performance is the result of a highly reversible reduction/oxidation of the polysulfides, synergistic effects between porosity and specific surface area, resulting in a negligible polysulfide shuttle. The presence of nitrogen atoms improves the capacity of SPVP as compared to nitrogen-free SPS, as the thioamide (-S-C=N) groups in SPVP facilitate reversible reduction/oxidation by serving as docking sites for polysulfide recuperation during recharge. Computational studies suggest that in SPVP, the discharge process involves Li+ coordination at N sites, while thioamide groups promote Li2S nucleation, resulting in a more favorable Gibbs free energy profile throughout all steps, up to full discharge, compared to SPS. Overall, the results highlight the key role of nitrogen atoms, which contribute to the superior performance of SPVP.