Energy systems digitalisation represents the energy sector's future, and Digital Twins represent the most advanced and complete way to monitor and optimally manage a complex system such as the upcoming solutions. Those latter will comprehend several energy generators, traditional and/or from renewable energy sources (RESs), different energy storage systems using several energy vectors and that interconnect different energy-consuming sectors (power, thermal, transport sectors) and that fully exploit the potential synergies offered by such interconnected system. Nevertheless, since the first conceptualisation of digital twins in the first years of the 21st century, its use has not started yet for different reasons that are affecting the adoption of this game-changer approach. Hence, what are the main barriers that are holding back the adoption of digital twins in smart energy systems? The present review paper answers this research question while discussing the case studies that can be found in literature and analysing the different approaches and the system architectures that have been tested or simply idealised. This paper provides a basis for future research that aims at applying the digital twin concept in the energy sector and particularly for power grid management. It deals with the challenges of big data management, the ones related to real-time measurements and continuous communication between the real-world system and its digital twin, the investment for measuring systems, the issues connected with the use of large data centres and the correlated energy-related challenges and doubts. The review analyses the challenges that have been encountered so far, the proposed solutions and the opportunities that such a 'work in progress' topic offers.