The objective of this proposal is to develop 3-dimensional hierarchical mesoporous nanocarbon architecture using primarily our unique holey nanocarbon platforms (holey graphene and holey carbon nanotubes) as air electrodes for high performance lithium-air batteries (LABs), or "breathing batteries", with ultrahigh energy density. Holey nanocarbon (HNC) platforms have recently demonstrated great promise in the application as high-performance electrodes for lightweight and compact supercapacitors (http://nari.arc.nasa.gov/ylin). These novel HNC structures exhibited not only micropores (< 2 nm), but also mesopores (2 - 50 nm) with controllable size and distribution. Mesopores of electrode materials are known to be critical to electrochemical energy storage. Different from conventional porous carbons, the HNCs have pores directly "carved" out from the sp2 graphitic carbon surfaces of graphene and carbon nanotubes, allowing pathways for efficient ion transport even when the lightweight electrode is highly densified for volume reduction. While graphene and carbon nanotubes have shown significant advantages over conventional porous carbons in energy storage, HNCs have shown superior performance due to the improved porous structure and beneficial chemistry that occurs as a consequence of hole creation. A unique advantage of HNCs in comparison with other porous carbon/nanocarbon systems is that the chemistry at the hole edges allows for further chemical modification, for example, with metal or metal oxides that can provide a favorable environment for the requisite oxidation/reduction reactions in the battery. LABs have a theoretical energy density of 3500 - 5000 Wh/kg, nearly 10 times that of conventional LIBs. Because the oxygen reactant on the cathode can be directly obtained from air, significant cost and weight reduction of the battery can be obtained. A set of challenges, very different from those encountered in supercapacitor research, are preventing the practical application of LABs. Increasing the catalytic efficiency of air cathode toward oxygen evolution to improve not only specific capacitance of air cathode but also its round-trip efficiency is a major challenge. Other major challenges include how to optimally induce the formation of resistive lithium peroxide discharge products with retaining the air diffusion, and how to maximize conductive contact between discharge products and air cathode for improved efficiency and cycling life. Based on recent results from the current Principal Investigators, using HNC platforms as essential elements for 3D porous, conductive electrode architecture with high surface area, controlled mesopore distribution, and unique hole edge chemistry is proposed to have significant potential to improve electrode performance by benefiting the creation of active catalytic sites, alleviate the air blocking of the cathode for mass transfer, and improve the electrical contact of resistive discharge product and conductive carbon support. As a result, the HNC cathode-based LABs would have (1) reduced cell overpotential, (2) elongated cycling life, (3) improved discharge-charge power and energy densities, and (4) improved volumetric performance.