A Digital Twin (DT) refers to a digital replica of physical assets, processes and systems. DTs integrate artificial intelligence, machine learning and data analytics to create living digital simulation models that are able to learn and update from multiple sources, and to represent and predict the current and future conditions of physical counterparts. However, the current activities related to DTs are still at an early stage with respect to buildings and other infrastructure assets from an architectural and engineering/construction point of view. Less attention has been paid to the operation & maintenance (O&M) phase, which is the longest time span in the asset life cycle. A systematic and clear architecture verified with practical use cases for constructing a DT would be the foremost step for effective operation and maintenance of buildings and cities. According to current research about multi-tier architectures, this paper presents a system architecture for DTs which is specifically designed at both the building and city levels. Based on this architecture, a DT demonstrator of the West Cambridge site of the University of Cambridge was developed, which integrates heterogeneous data sources, supports effective data querying and analysing, supports decision-making processes in O&M management, and further bridges the gap between human relationships with buildings/cities. This paper aims at going through the whole process of developing DTs in building and city levels from the technical perspective and sharing lessons learnt and challenges involved in developing DTs in real practices. Through developing this DT demonstrator, the results provide a clear roadmap and present particular DT research efforts for asset management practitioners, policymakers and researchers to promote the implementation and development of DT at the building and city levels.