Recent scientific and technological advancements have transformed the knowledge frontiers, giving rise to the next wave of disruptive technologies with deep impacts on urban society. An Urban Digital Twin (UDT) is a technology with great potential to transform the management and planning of the infrastructures and systems of sustainable smart cities towards environmental sustainability. However, despite the recent increase of research on UDTs due to its widespread diffusion much more recently, there is a lack of studies examining the existing bottlenecks to its implementation. To fill this gap, this study provides a systematic literature review on the key challenges and open issues pertaining to the implementation of an UDT. Results indicate 8 important categories of challenges related to (1) interoperability and semantics; (2) infrastructure, including storage, computation, network; (3) data acquisition and actuation; (4) data quality and harmonization; (5) modeling, simulation and decision-support; (6) data visualization and information display; (7) human and capital resources; and finally (8) governance, organizational and social issues. All topics are significantly raised in the literature, with most emphasis on issues pertaining to data and model semantics, missing data, data quality and modeling. The findings serve to inform practitioners about the bottlenecks delaying the implementation of UDTs.