Due to its excellent electronic, optical, thermal and mechanical properties, and its large surface area and low mass, graphene holds great potential for a wide range of applications. It seems that the research in graphene has now proceeded from the initial phase of developing myriad strategies for the synthesis of graphene sheets to the use of graphene in various research fields. Mass production of reduced graphene oxide and graphene nanoplatets has recently been achieved. However, it is still challengingto controllably produce solution processable highly conductive graphene sheets in large quantity, at low cost, via eco-friendly and energy saving process, with optimal sheet size, layer thickness, defective (vacancies and holes) and molecular structures (oxygen containing groups and non-defective graphene domains). All these structural parameters determine their electronic, thermal and mechanical properties of graphene, which are the key warrants for their practical application in various devices. As examples, fundamental studies and high-frequency electronics require pristine graphene. However, “bulk” applications such as flexible macroelectronics, and mechanically and electronically reinforced composites, require large quantities of solution-processible highly conductive large graphene sheets manufactured at low cost. On the other hand, holey graphene, referred to graphene with nanoholes in their basal plane, demonstrates much better performance in their application as metal free catalysts and in energy storage. Finally, there is a surge of interests in nanosized graphene sheets for solar cells and various biological applications due to their unique size effects, edge effects, and even quantum confinement effects. Most importantly, most of the commercial available solution processible graphene sheets were fabricated via a long multiple- step process (several hours to 5 days). By exploiting the unique thermal and kinetic effects induced by microwave heating and the right selection of graphite oxidation chemistry, we developed series of quick and scalable strategies to produce a family of “clean” graphene sheets (without surfactants and without metal ions and/or toxic residues) with controlled porous structures, and controlled sizes from a few nanometers to tens of micrometers. By choosing a series of cheap biomass molecules, also with the help of microwave heating, bottom-up fabrication approaches are developed to produce heteroatom (N, B and/or P) doped graphene sheets and graphene quantum dots with bright emission. The applications of these graphene sheets and graphene quantum dots in Lithium battery, metal free-catalysts, and multifunctional drug delivery will be discussed.