The global energy demand calls for more efficient storage systems. In this review, the state of the art of Li/air and Li/O2 batteries is discussed with particular attention on the more recent findings regarding all the battery compartments. Both aqueous and non-aqueous systems are considered, and the most critical issues for better battery design are addressed. Whereas the predicted charge/discharge values for these devices do justify the intense research efforts performed nowadays, great problems are still present which must be overcome in order to make Li/air and Li/O2 a reality for future large-scale applications.