In recent years, the concept of the Circular Economy has acquired greater traction, both in the research community and in wider society, as an instrument that provides innumerable methodologies with which to face the environmental, social, and environmental challenges caused by the linear production model. This study focuses on analyzing the degree of advancement of the Circular Economy in the scientific field through a bibliometric analysis (or scientometrics) of 5,007 research articles available in Scopus database and published during the period 2005–2007. The main research characteristics are presented, and the Paris Climate Conference (COP21), held on December 12, 2015, is highlighted as a key driver of this particular line of research. The analysis revealed the main authors, journals, subject area, countries and current and future lines of research, finding that the Circular Economy is a paradigm with environmental, economic and social implications, both for the productive system and for consumers.