The significance of graphene and its two-dimensional (2D) analogous inorganic layered materials especially as hexagonal boron nitride (h-BN) and molybdenum disulphide (MoS2) for "clean energy" applications became apparent over the last few years due to their extraordinary properties. In this review article we study the current progress and selected challenges in the syntheses of graphene, h-BN and MoS2 including energy storage applications as supercapacitors and batteries. Various substrates/catalysts (metals/insulator/semiconducting) have been used to obtain graphene, h-BN and MoS2 using different kinds of precursors. The most widespread methods for synthesis of graphene, h-BN and MoS2 layers are chemical vapor deposition (CVD), plasma-enhanced CVD, hydro/solvothermal methods, liquid phase exfoliation, physical methods etc. Current research has shown that graphene, h-BN and MoS2 layered materials modified with metal oxide can have an insightful influence on the performance of energy storage devices as supercapacitors and batteries. This review article also contains the discussion on the opportunities and perspectives of these materials (graphene, h-BN and MoS2) in the energy storage fields. We expect that this written review article including recent research on energy storage will help in generating new insights for further development and practical applications of graphene, h-BN and MoS2 layers based materials.