Since the discovery of the promising properties of graphene, research in the field has attracted numerous grants and sponsors, leading to an exponential rise in the number of papers and applications. This article presents a global map of graphene research and its intellectual structure, drawn using the terms of more than 50,000 documents extracted from Scopus database, years 1998-2015. The unit of analysis consisted of descriptors (including Author Keywords and Indexed Keywords), with the co-occurrence of descriptor as the unit of measure, using fractional counting. The main research lines identified are: Fundamental Research, Functionalization and Biomedical Applications, Technology and Devices, Materials Science, Energy Storage, Optics and Chemical Properties and Sensors. Using overlay maps, we depict the graphene research efforts of the United States, the European Union (Europe-28), and China, and project their evolution through longitudinal maps to facilitate comparison. The United States was initially at the head of world output in graphene research, but was surpassed by China in 2011 and by Europe in 2014, as a result of their respective scientific policies and financial support. The output of China has since been so intense that it can be said to mark graphene research trends. We believe this information may be valuable for the core community involved in this scientific field, as it offers a large-scale analysis showing how research has changed over time. It is therefore also helpful for policy makers and research planners. The resulting maps are a useful and attractive tool for the graphene research community, as they reveal the main lines of exploration at a glance. The methodology described here could be re-created in any other field of science to uncover and display its intellectual structure and evolution over time.