Growing environmental concerns and increasing demand for energy have stimulated extensive interest in electrical energy storage. Li-air batteries are appealing in this regard as they offer much higher energy density than the current Li-ion batteries, but the nonaqueous Li-air batteries suffer from poor cycle life arising from electrolyte decomposition and clogging of the air electrode by insoluble discharge products. Interestingly, hybrid Li-air batteries in which a solid electrolyte separates the lithium-metal anode in an aprotic electrolyte from the air electrode in an aqueous catholyte could overcome these problems. Lots of efforts have been made on developing efficient bifunctional catalysts to lower the overpotential and improve the stability of hybrid Li-air batteries, but the cycle life is still limited. This dissertation focuses on the development of advanced cell configurations and high-performance catalysts for hybrid Li-air batteries. First, a buffer catholyte solution with a moderate pH, based on phosphoric acid and supporting salts, has been developed to keep the solid electrolyte stable and reduce the internal resistance and overpotential. With a high operating voltage and the utilization of all the three protons of phosphoric acid, the buffer catholyte enables a Li-air cell with high energy density. Further increase in power density has been realized by increasing the solid-electrolyte conductivity and operating temperature to 40 °C. The biggest challenge with Li-air cells is the large overpotentials associated with the oxygen reduction reaction (ORR) and oxygen evolution reaction (OER). Noble-metal-free NiCo₂O₄ nanoflakes directly grown onto a nickel foam (NCONF@Ni) has been found to exhibit high OER activity that is comparable to that of the expensive, noble-metal IrO₂ catalyst. Furthermore, a novel 3-D O- and N-doped carbon nanoweb (ON-CNW) has been developed as an inexpensive, metal-free catalyst for ORR. With a hybrid Li-air cell, the ON-CNW exhibits performance close to that of commercial Pt/C. In addition, a novel hybrid Li-air cell configuration with decoupled ORR and OER electrodes has been developed. The hybrid Li-air cell with decoupled ORR and OER electrodes eliminates the degradation of ORR catalysts and carbon support in the highly oxidizing charge process and leads to high efficiency with good cycle life. / text