Today's lithium (Li)-ion batteries have been widely adopted as the power of choice for small electronic devices through to large power systems such as hybrid electric vehicles (HEVs) or electric vehicles (EVs). However, it falls short of meeting the demands of new markets in these areas of EVs or HEVs due to insufficient energy density. Therefore, new battery systems such as Li-air batteries with high theoretical specific energy are being intensively investigated, as this technology could potentially make long-range EVs widely affordable. So far, Li-air battery technology is still in its infancy and will require significant research efforts. This review provides a comprehensive overview of the fundamentals of Li-air batteries, with an emphasis on the recent progress of various elements, such as lithium metal anode, cathode, electrolytes, and catalysts. Firstly, it covers the various types of air cathode used, such as the air cathode based on carbon, the carbon nanotube-based cathode, and the graphene-based cathode. Secondly, different types of catalysts such as metal oxide- and composite-based catalysts, carbon- and graphene-based catalysts, and precious metal alloy-based catalysts are elaborated. The challenges and recent developments on electrolytes and lithium metal anode are then summarized. Finally, a summary of future research directions in the field of lithium air batteries is provided.