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Building electronic devices based on graphene has been motivating intense research. Field-effect transistors have been demonstrated, but graphene also holds promise as interconnect, since it can sustain very high current density. Such current-carrying capacities are several orders of magnitude higher than that of present-day interconnects. Thermal/electrical transport-properties and charge carrier dynamics after optical excitations are ruled by the electron and phonon scattering. In order to unravel the capabilities and the limits of graphene devices to sustain very high current density, I will present a detailed analysis of the electron and phonon scattering processes based on both first-principles electronic-structure calculations and experimental phonon measurements. Such detailed knowledge of the electron-phonon and phonon-phonon interactions has allowed us to study both the thermal conductivity and the origin of charge-current saturation in graphene at high field in the framework of Boltzmann transport theory.