Increased changes in the climate and ecosystems call for a sustainable economic development, where economic growth should be compatible with the environment goals. In order to do this, it is urgent to find new ways of life and new production systems that make our ecological footprint compatible with global sustainability. The concept of the circular economy has brought relevant contributions to this problem. The central objective of the study presented here is to highlight the main insights presented through scientific literature about the concept of the circular economy within the European Union. In practice, the intention is to show what has already been done about this topic and what can/should be implemented in the future. To achieve these objectives, 144 articles were considered from the Web of Science (Core Collection) for the topics “circular economy” and “European Union”. These documents were, firstly, analysed through a proper literature review and later explored through bibliometric analysis, considering bibliographic data and the VOSviewer software. As the main findings have revealed, the increased importance of this concept within the European Union is recognized. However, this paper also identifies several challenges in the literature, namely the concentration of the identified publications in certain countries, organizations, and authors.