Circular economy goals have made their way towards the very heart of EU policy, promising the delivery of both economic and environmental goals, but key to their achievement is the active involvement and participation of businesses. Scholarly literature has made considerable headway in describing the diverse CE business model archetypes and the enablers and barriers that can nurture the transition toward them. However, little work has been done to assess a more profound distinction—that between enterprises that are born circular in contrast with incumbent businesses that grow into circularity. We review 18 case studies of businesses in Europe, which shed light on this distinction. A systematic analysis of their internal, contextual, and policy issues results in the identification of ten key enablers (including business targets, cost reduction potential, loyal customers, demographic aspects, growing waste flows, environmentalism, EU policy, circular policy, and dis/incentives as well as sectoral considerations) and ten key barriers (including bottom line concerns, problematic consumer preferences, lack of infrastructure, technological barriers, poor access to finance, competition, lack of EU harmonisation, uncertainty and lack of internalisation of externalities, and the presence of obstructive policy). We observe that businesses which are born circular seem to face fewer barriers than those seeking to grow into circularity, a finding which offers hope for the transition to a circular economy. Our analysis also suggests that while some enablers and barriers cut across different types of businesses, others tend to be more prevalent among enterprises of a certain size or sector.