Oceans cover more than 70% of the Earth’s surface. For various reasons, almost 95% of these areas remain unexplored. Underwater wireless communication (UWC) has widespread applications, including real-time aquatic data collection, naval surveillance, natural disaster prevention, archaeological expeditions, oil and gas exploration, shipwreck exploration, maritime security, and the monitoring of aquatic species and water contamination. The promising concept of the Internet of Underwater Things (IoUT) is having a great influence in several areas, for example, in small research facilities and average-sized harbors, as well as in huge unexplored areas of ocean. The IoUT has emerged as an innovative technology with the potential to develop a smart ocean. The IoUT framework integrates different underwater communication techniques such as optical, magnetic induction, and acoustic signals. It is capable of revolutionizing industrial projects, scientific research, and business. The key enabler technology for the IoUT is the underwater wireless sensor network (UWSN); however, at present, this is characterized by limitations in reliability, long propagation delays, high energy consumption, a dynamic topology, and limited bandwidth. This study examines the literature to identify potential challenges and risks, as well as mitigating solutions, associated with the IoUT. Our findings reveal that the key contributing elements to the challenges facing the IoUT are underwater communications, energy storage, latency, mobility, a lack of standardization, transmission media, transmission range, and energy constraints. Furthermore, we discuss several IoUT applications while highlighting potential future research directions.