Electrical energy storage system such as secondary batteries is the principle power source for portable electronics, electric vehicles and stationary energy storage. As an emerging battery technology, Li-redox flow batteries inherit the advantageous features of modular design of conventional redox flow batteries and high voltage and energy efficiency of Li-ion batteries, showing great promise as efficient electrical energy storage system in transportation, commercial, and residential applications. The chemistry of lithium redox flow batteries with aqueous or non-aqueous electrolyte enables widened electrochemical potential window thus may provide much greater energy density and efficiency than conventional redox flow batteries based on proton chemistry. This Review summarizes the design rationale, fundamentals and characterization of Li-redox flow batteries from a chemistry and material perspective, with particular emphasis on the new chemistries and materials. The latest advances and associated challenges/ opportunities are comprehensively discussed.