Graphene is the most widely investigated carbon nanomaterial having two-dimensional honeycomb lattice structure. Recently, it has attracted worldwide attention due to its remarkable electrical, thermal, mechanical, chemical and optical properties, which are highly suitable for various electronic device applications. Various methods of graphene synthesis have been utilized for the production of graphene each having its own advantages and disadvantages. Liquid phase exfoliation method uses top-down approach and has the advantages of being environment friendly, facile and economically viable. Liquid phase exfoliated graphene is highly suitable for making thin films for their potential applications in electronic devices such as thin films transistors, transparent electrodes, light-emitting diodes, supercapacitors, etc. In this paper, a comparative study of different exfoliation medium used for liquid phase exfoliation of graphene such as organic solvents, ionic liquids, surfactants, polymers and acids are described. Because of the usually low concentration of graphene (< 0.01 mg/mL) obtained from liquid phase exfoliation method, research has been done for enhancing the concentration. Recent progress made in enhancing graphene concentration in organic solvents by adding various additives is reported here. Finally, we discuss the challenges and future prospects of improving liquid phase exfoliation of graphene for modern electronics devices.