After discovering the promising properties of graphene, the research in the field is attracting large grants and sponsors with an exponential rise in the number of papers and applications. This paper presents a global map of graphene research and its intellectual structure through the terms of more than 50,000 documents extracted from Scopus database from 1998 to 2015. The unit of analysis has been the descriptors (including Authors keywords and Indexed keywords) and its co-occurrence, using fractional counting, as unit of measure. The main research lines identified are: Fundamental Research, Functionalization and Biomedical Applications, Technology and Devices, Material Sciences, Energy Storage, Optics and Chemical Properties and Sensors. Using overlay maps we show the graphen research of USA, Europe-28, China and their evolution through longitudinal maps, comparing them. USA begins leading the world output in graphene, but is surpassed by China in 2011 and Europe in 2014, as a result of stimulus policies and financial support. The output of China is so intense from that year on, that it is difficult to understand the recent world scientific production in graphene without its participation, marking the research trends in some cases. We believe that this information may be very useful for the scientific community involved in this field as it reflects a large-scale analysis how research has changed over time, and for helping policimakers in research planning. This study is moreover intended to offer a useful tool for the graphene scientific community, revealing at a glance the main research lines. The methodology can be replicated in any other field of science to explore its intellectual structure and its evolution.