The operation and maintenance (O&M) of buildings and infrastructure represent a strategic activity to ensure they perform as expected over time and to reduce energy consumption and maintenance costs at the urban and building scale. With the increasing diffusion of BIM, IoT devices, and AI, the future of O&M is represented by digital twin technology. To effectively take advantage of this digital revolution, thus enabling data-driven energy control, proactive maintenance, and predictive daily operations, it is vital that smart building management exploits the opportunities offered by the extended reality (XR) technologies. Nevertheless, in consideration of the novelty of XR in the AECO sector and its rapid and ongoing evolution, knowledge of the specific possibilities and the methods of integration into the building process workflow is still piecemeal and sparse. With the goal to bridge this gap, the article presents a thorough review of virtual reality (VR), augmented reality (AR), and mixed reality (MR) technologies and applications for smart building operation and maintenance. After defining VR, AR, and MR, the article provides a detailed review that analyzes, categorizes, and summarizes state-of-the-art XR technologies and their possible applications for building O&M along with their relative advantages and disadvantages. The article concludes that the application of XR in building and city management is showing promising results in enhancing human performance in technical O&M tasks, in understanding and controlling the energy efficiency, comfort, and safety of building and infrastructures, and in supporting strategic decision making for the future smart city.