Single-layer graphene (SLG) membranes, hosting molecular-sieving nanopores have been regarded as the ultimate gas separation membranes, attributing to the fact that they are the thinnest possible molecular barrier. However, the expected attractive performance for gas separation from one-atom-thick graphene membranes has rarely been demonstrated experimentally. There are two major bottlenecks to realize this high-performance graphene membrane: 1) crack-free fabrication of large membrane area; 2) incorporation of high-density nanopores with a narrow pore-size distribution in the otherwise impermeable graphene lattice. This dissertation focuses on the development of a crack-free transfer method and highly-precise pore-etching chemistry to realize high-performance single-layer graphene membranes for gas separation. A novel nanoporous carbon-assisted transfer method was developed to mechanically reinforce the atom-thick graphene layer during its transfer from catalytic Cu foil to a porous substrate, yielding a relatively large area (millimeter-scale) crack-free graphene membrane. This enabled, for the first time, the observation of the gas-sieving behavior through the intrinsic defects in the chemical vapor deposition (CVD) derived polycrystalline SLG. Attractive H2 permeance and molecular-sieving selectivity between H2 (kinetic diameter of 2.89 Å) and CH4 (kinetic diameter of 3.80 Å) were achieved by the graphene film. A scalable gas-phase millisecond ozone-based carbon gasification chemistry was developed to realize a controllable etching of graphene lattice. High-density (1012 cm-2) gas-sieving nanopores with narrow pore-size distribution were observed by scanning tunneling microscopy and aberration-corrected high-resolution transmission electron microscopy. A model based on the kinetics of ozone etching was built to optimize the incorporation of CO2-sieving pores on graphene. The nanoporous single-layer graphene (N-SLG) membranes accomplished an effective separation between CO2 (3.30 Å) and O2 (3.46 Å), corresponding to 0.2 Å molecular sieving resolution. Furthermore, ozone-based pore-edge functionalization chemistry and oxygen-based slow etching method were developed to adjust the molecular cut-off within the sub-angstrom for tuning the gas separation performance. The resulting N-SLG membrane reached O2/N2 selectivity of 3.4 with corresponding O2 permeance of 1300 gas permeation units (GPU; 1 GPU = 3.35"×" 10-10 mol m-2 s-1 Pa-1), and CO2/N2 selectivity of 21.7 with corresponding CO2 permeance of 11850 GPU. These are, so far, the best membrane performance for the post-combustion carbon capture, and will likely tilt the capture technology toward the membrane-based process. The developed transfer method and ozone-based pore-edge functionalization chemistry are universal tools for high-performance carbon-based membrane fabrication. Accordingly, a sub-200 nm defect-free carbon molecular sieve membrane was successfully fabricated with a tunable pore-size distribution, resulting in attractive gas separation performance as well.