A method of producing exfoliated graphite or graphene from a graphitic or carbonaceous material. The method includes: (a) dispersing a graphitic material in a liquid intercalating agent to form a suspension; and (b) subjecting the suspension to microwave or radio frequency irradiation for a length of time sufficient for producing the exfoliated graphite or graphene. In one preferred embodiment, the intercalating agent is an acid or an oxidizer, or a combination of both. The method enables production of more electrically conducting graphene sheets directly from a graphitic material without going through the chemical intercalation or oxidation procedure. The process is fast (minutes as opposed to hours or days of conventional processes), environmentally benign, and highly scalable.