Creativity represents a young and promising academic field of research. Over the last 20 years, creativity publications have been steadily increasing in number. Of the 20 most all-time prolific creativity scholars in the European Union (EU), only one has retired. The present paper aims at mapping the EU creativity research. We analyzed over 12,000 Web of Science records dated back to 1968 until December 2020, using two bibliometric tools, SciMAT and VOSviewer. The descriptive analysis lists the most prolific authors and journals on the creativity area, the most cited articles, as well as the authors', institutions', countries', and research areas' bibliometric networks. Moreover, this study presents a thematic analysis and an evolution map of the themes based on keywords. The EU scholars were found to establish collaborations based on geographical, cultural, and, maybe, idiomatic proximity. Engineering, computer science, and education & educational research are the most interconnected areas of research. Innovation, performance, creative cities, the neuroscientific study of creativity, and emotions are relevant topics in the area. A broader concept of the creative and collaborative economy, the impact of technology on developing creativity, and the study of the brain with neuroscientific tools may become promising lines for future research.