In this presentation, I will introduce the fundamental and the most recent and significant scientific progresses made in the fields relevant to Zn-air and Li-air batteries, with emphasis placed on air electrodes. The preparation of MnO2 nanotubes functionalized with Co3O4 nanoparticles and their use as bifunctional air cathode catalysts for oxygen reduction reaction and oxygen evolution reaction in rechargeable zinc-air batteries will be reported. These hybrid MnO2/Co3O4 nanomaterials exhibit enhanced catalytic reactivity toward oxygen evolution reaction in alkaline conditions compared with that in the presence of MnO2 nanotubes or Co3O4 nanoparticles alone. Other bifunctional catalysts for oxygen reduction and evolution reactions in Zn-air batteries include spinel MnCo2O4/ nanocarbon hybrids, perovskite lanthanum cobalt manganese oxides/nanocarbon hybrids (LCMO/NC), Co3O4 nanoparticles decorated carbon nanofiber and cobalt sulphide/N- or S-doped grapheme etc. I also will report porous cobalt-manganese oxide nanocubes derived from metal organic frameworks and porous perovskite LaNiO3 nanocubes as cathode catalysts for rechargeable Li-O2 batteries.