The UK construction industry (CI) has made significant progress in recovering non-hazardous construction and demolition waste (CDW). Nevertheless, construction is still responsible for 60% (130 MT/year) of all waste produced. There have been claims in the literature that Industry 4.0 technologies have the potential to support the transition to a circular economy (CE); however, these claims have yet to be tested in the construction context. A systematic literature review including 31 hits was conducted to explore the potential of Industry 4.0 technologies, referred to as Construction 4.0, for supporting the transition to CE in construction and to identify barriers to their adoption. Findings revealed that the adoption of Construction 4.0 is still associated with technical and managerial barriers and requires the involvement of all stakeholders. The most prominent technical barriers were the lack of standards, fragmented data-sharing platforms and individual technologies’ lack of holistic capability for solving CE problems. The costs of purchase, implementation, training, maintenance and operation were prominent among the managerial barriers. Overall, Construction 4.0 solutions were limited to separate situations and did not support circularity throughout the whole construction process. Hence, a framework was developed mapping technologies to different stages in the construction process where they can support circularity. Future research will seek to develop a model to systematically employ Construction 4.0 technologies throughout the construction process to enhance its circularity.