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A comprehensive study of electrostatic discharge (ESD) characterization of atomically thin graphene is reported. In a material comprising only a few atomic layers, the thermally destructive second breakdown transmission line pulsing (TLP) current (It2) reaches a remarkable 4 mA/μm for 100-ns TLP and ~8 mA/μm for 10-ns TLP or an equivalent current density of ~3 × 108 and 4.6 × 108 A/cm2, respectively. For ~5-nm thick (~15 layers) graphene film, It2 reaches 7.4 mA/μm for 100-ns pulse. The fact that failure occurs within the graphene and not at the contacts indicates that intrinsic breakdown properties of this new material can be appropriately characterized using short-pulse stressing. Moreover, unique gate biasing effects are observed that can be exploited for novel applications including robust ESD protection designs for advanced semiconductor products. This demonstration of graphene's outstanding robustness against high-current/ESD pulses also establishes its unique potential as transparent electrodes in a variety of applications.