The circular economy (CE) has recently emerged as a key strategy for promoting sustainability and reducing waste in various industrial sectors. This paper provides an overview of the definition, assessment and enhancement of circularity in general and in five key industries, including aerospace, wind energy, transportation, automotive and sports goods, by using data and information from the literature and for the section of the definitions of the CE also using information from the EC funded project “RECREATE”. The survey reviews in detail the different definitions, assessment methods and metrics used to explore and evaluate circularity, including assessment frameworks such as Life Cycle Assessment (LCA) and assessment indicators. Furthermore, it explores the challenges, possibilities and available tools for enhancing circularity, focusing on digital tools. The survey highlights the importance of a holistic and systemic approach to circularity concerning all stakeholders along the value chain. Overall, this study aims to contribute to a better understanding of the circular economy's definition, assessment, and enhancement and provides insights for future research.