Conducting composite current collector for a battery or supercapacitor and production process

Provided is a composite thin film current collector for a battery or supercapacitor, the thin film comprising graphene sheets dispersed in or bonded by an electron-conducting polymer network (also referred to as conducting network polymer, crosslinked polymer, or hydrogel polymer) wherein the composite thin film has a thickness from 2 nm to 500 μm and an electrical conductivity from 10to 10S/cm and wherein the graphene sheets occupy from 10% to 99% by weight and the polymer network from 1% to 90% by weight of the total composite weight.