Building energy management systems (BEMSs) have been successfully adopted as key control units for modern structures to maintain energy efficiency and provide a comfortable thermal environment for occupants. Recent advances in information and communication technology toward “Industry 4.0” are enhancing the utility of BEMSs. However, challenges, such as how to process the exponentially growing amount of heterogeneous data generated in buildings, need to be addressed to realize “Building 4.0,” which encompasses next-generation smart systems that provide user-centric services. In this article, we propose BEMS–Edge, a framework that integrates seamless, real-time information acquisition, transmission, interpretation, and action in intelligent BEMSs. The primary components, including the Internet of Things (IoT), cloud/edge computing, big data analytics, and artificial intelligence (AI), converge to create a data-driven edge computing fabric offering a range of benefits, such as real-time data analytics and cost savings. The effectiveness of BEMS–Edge is verified by an established, real-world BEMS testbed.