Every few years, a novel material with salient and often unique properties emerges and attracts both academic and industrial interest from the scientific community. The latest blockbuster is graphene, an increasingly important nanomaterial with atomically thin sheets of carbon, which has become a shining star and has shown great promise in the field of material science and nanotechnology. In recent years, it has changed from being the exclusive domain of physicists to the new passion of chemists and biologists. Graphene and its derivatives are now at the forefront of nearly every rapidly developing field of science and engineering, including biochemistry, biomedicine and certain cutting-edge interdisciplines that have intense popularity. The aim of this review is, firstly, to provide readers with a comprehensive, systematic and in-depth prospective of graphene's band structure and properties, and secondly, to concentrate on the recent progress in producing graphene-based nanomaterials, including mechanical exfoliation, chemical vapor deposition, plasma enhanced chemical vapor deposition, chemical reduction of graphene oxide, total organic synthesis, electrochemical synthesis and other fabrication strategies widely accepted by research scientists. At the same time, important definitions related to graphene are also introduced. The focus of this Tutorial Review is to emphasize the current situation and significance of using this new kind of two-dimensional material in the hot and emerging fields that are closely related to human life quality, for instance, cell biochemistry, bioimaging along with other frontier areas. Finally, the latest developments and possible impact that affect the heart of the whole scientific community have been discussed. In addition, the future trends along with potential challenges of this rapidly rising layered carbon have been pointed out in this paper.