Industry 4.0 represents the fourth industrial revolution and is the digital transformation of smart manufacturing and industrial markets. In the Industry 4.0 era, emerging technologies such as the Internet of Things (IoT), cloud computing, big data, blockchain, 5G, and digital twins have arisen rapidly. Most of them are utilized in supply chain management processes, leading to the rise of digital supply chains. The most widely used technology is IoT. The most common applications are the technologies combined with IoT, cloud computing, and big data analysis. Blockchain is a developing technology, while the digital supply chain twins are an integrated technology encompassing simulation. Thus, this review focuses on these four critical technologies (i.e., IoT, big data, blockchain, and digital supply chain twins) to explore their principles, applications, and possible challenges in the digital supply chain. In addition, this review also compares the difference between digital supply chains and smart supply chains and explains their relationship.