Construction is a major source of carbon emissions. Moreover, it faces various other sustainability challenges, such as construction waste, construction noise, vehicular traffic near construction sites, dust and other air and water pollutants, and safety and well-being of construction workers. Poorly designed and constructed buildings will continue to affect the well-being of their occupants and overall energy efficiency throughout the building lifecycle. Hence, accelerating the transformation of the construction industry towards smart construction or Construction 4.0 is an important topic. The ways that technology can help to achieve smart construction, especially with the adoption of construction methods with increasing construction modularity, should be further explored. Focusing on modular integrated construction (MiC), this paper examines the following questions: (1) How has technology been applied to support MiC development and smart construction in Hong Kong? (2) What are the lessons learned? A case study approach of a building information model (BIM)-enabled multifunctional blockchain-based digital platform is adopted to allow us to systematically consider (1) the main objectives and scope, (2) the stakeholders involved, (3) the key outcomes and processes, (4) the applications of blockchain technology, and (5) the integration with other digital software and management platforms in practice. Drawing upon the experience, we propose a generic four-stage approach in understanding and facilitating the adoption of relevant technology towards smart construction. At Stage One, the technologies of BIM, RFID, and blockchain are applied to support the core elements of MiC production: just-in-time transportation and on-site installation. At Stage Two, the digital platform is extended to serve as an interface for third parties, notably government; monitoring, authentication, and certifications for information sharing; visualization; and real-time monitoring and updating of MiC projects. At Stage Three, the system focuses on people in the construction process, aiming to enhance the safety and well-being of workers and drivers throughout the construction process. Different Internet-of-Thing devices and sensors, construction robotics, closed-circuit television, dashboards, and cloud-based monitoring are deployed. At Stage Four, the full construction lifecycle is the focus, whereby a centralized smart command theatre is set up with multiple sources of data in a city information model.