The metaverse, as an envisioned paradigm of the future internet, aims to establish an immersive and multidimensional virtual space in which global users can interact with one another, as in the real world. With the rapid development of emerging technologies—such as digital twins (DT), blockchain, and artificial intelligence (AI)—the diverse potential application scenarios of the metaverse have attracted a great deal of research attention and have created a prosperous market. The demand for ubiquitous communications, pervasive sensing, ultra-low latency computing, and distributed storage has consequently surged, due to the massive heterogeneous devices and data in the metaverse. In order to achieve the metaverse, it is essential to establish an infrastructure system that integrates communications, sensing, computing, and storage technologies. Information about the physical world can be obtained by pervasive sensing, computing resources can be scheduled in a reasonable manner, quick data access can be achieved through the coordination of centralized and distributed storage, and, as the bridge, mobile communications systems connect communications, sensing, computing, and storage in a new system, which is the integration of communications, sensing, computing, and storage (I-CSCS). Following this trend, this paper discusses the requirements of the metaverse for spectrum resources, ultra-reliable transmission, seamless coverage, and security protection in wireless mobile communications systems, and analyzes the fundamental supporting role of the sixth-generation mobile communications system (6G) in the metaverse. Then, we explore the functions and roles of the integrated sensing and communications technologies (ISAC), as well as the integration of communications, computing, and storage technologies for the metaverse. Finally, we summarize the research directions and challenges of I-CSCS in the metaverse.