The implementation of emerging technologies generates new possibility for the Architectural Engineering and Construction sector. Specifically, the study focuses on the applications of Digital Twins in the heritage construction sector, an area characterized by significant potentials and challenges in various research fields (e.g., energy, digital technology, citizen engagement, cultural aspects, management, etc.). Bibliographic and scientometric analyses enable the systematic categorization of the literature, analyzing a total of 133 scientific publication realized in the years 2001–2023. The bibliometric analysis outlines time evolution, geographical distribution, type, and disciplinary fields of the publications. Meanwhile, the scientometric research identifies co-occurrence networks of authors, keyworks, and research topics. Thank to these techniques, the following research topics on Digital Twins in the Built Heritage have been identified and clustered: (i) Digital Twins and 3D scanner techniques; (ii) Digital Twins and virtual reality; (iii) Digital Twins and Heritage Building Information Model (HBIM); and (iv) Digital Twins and Internet of Things (IoT). Each technique is critically discussed, highlighting applications, methods, limitations, and gaps in the literature. This analysis also paves the way for future research directions and potential solutions to enhance the automation in the heritage sector. Additionally, a glossary of essential disciplinary terms is provided to guide the understanding of individual definitions as they apply to heritage constructions. The primary challenges relate to accuracy, security, interoperability, and synchronization of data and technologies from various sources, requiring appropriate verification and validation methodologies, as well as tailored standards, protocols, interfaces, and regulations. Moreover, ethical considerations should underlie the utilization of digitally driven predictions that incorporate human-computer techniques, and human–robot interactions. This extends to the formulation of specific policies, and legislation. Only through this approach, the immense potential of digital technologies can emerge to create cross-cutting professions, interactive engagement techniques, and compatible preservation and management activities.