The sixth generation (6G) wireless communication networks are envisioned to revolutionize customer services and applications via the Internet of Things (IoT) towards a future of fully intelligent and autonomous systems. In this article, we explore the emerging opportunities brought by 6G technologies in IoT networks and applications, by conducting a holistic survey on the convergence of 6G and IoT. We first shed light on some of the most fundamental 6G technologies that are expected to empower future IoT networks, including edge intelligence, reconfigurable intelligent surfaces, space-air-groundunderwater communications, Terahertz communications, massive ultra-reliable and low-latency communications, and blockchain. Particularly, compared to the other related survey papers, we provide an in-depth discussion of the roles of 6G in a wide range of prospective IoT applications via five key domains, namely Healthcare Internet of Things, Vehicular Internet of Things and Autonomous Driving, Unmanned Aerial Vehicles, Satellite Internet of Things, and Industrial Internet of Things. Finally, we highlight interesting research challenges and point out potential directions to spur further research in this promising area.