Lithium-sulfur battery is one of the most promising systems for electric vehicles. Unfortunately, its application has been impeded by its slow charging/discharging rates, fast capacity degradation, and short cycling life. Although several materials have been identified as efficient adsorbents or mediators for lithium polysulfides, their working mechanism remains ambiguous. Here we report a systematic study of the interactions between transition metal oxides/sulfides and lithium polysulfides based on their electron structures. This study provides not only mechanistic insights into the fundamental issues associated with sulfur cathodes, but also offers quantified design framework for advanced lithium-sulfur batteries. Besides, we developed a class of regenerative polysulfide-scavenging layer and a series of polysulfide-mediators. The resulted cells exhibit high gravimetric energy densities, high power output and extended cycling lifetime, showing great promise for practical applications.