A digital twin is a computer-based “virtual” representation of a complex system, updated using data from the “real” twin. Digital twins are established in product manufacturing, aviation, and infrastructure and are attracting significant attention in medicine. In medicine, digital twins hold great promise to improve prevention of cardiovascular diseases and enable personalised health care through a range of Internet of Things (IoT) devices which collect patient data in real-time. However, the promise of such new technology is often met with many technical, scientific, social, and ethical challenges that need to be overcome—if these challenges are not met, the technology is therefore less likely on balance to be adopted by stakeholders. The purpose of this work is to identify the facilitators and barriers to the implementation of digital twins in cardiovascular medicine. Using, the Non-adoption, Abandonment, Scale-up, Spread, and Sustainability (NASSS) framework, we conducted a document analysis of policy reports, industry websites, online magazines, and academic publications on digital twins in cardiovascular medicine, identifying potential facilitators and barriers to adoption. Our results show key facilitating factors for implementation: preventing cardiovascular disease, in silico simulation and experimentation, and personalised care. Key barriers to implementation included: establishing real-time data exchange, perceived specialist skills required, high demand for patient data, and ethical risks related to privacy and surveillance. Furthermore, the lack of empirical research on the attributes of digital twins by different research groups, the characteristics and behaviour of adopters, and the nature and extent of social, regulatory, economic, and political contexts in the planning and development process of these technologies is perceived as a major hindering factor to future implementation.