As oceans cover the majority of the earth’s surface, it becomes inevitable in extending the concepts of Internet of Things (IoT) to ocean bodies, thereby tiling the way for a new drift in the digital world, the Internet of Underwater Things (IoUT). The primary objective of IoUT is the creation of a network of several smart interconnected undersea things, to digitally link water bodies by using devices such as autonomous underwater vehicles. Since the traditional ideas of IoT cannot be merely expanded to underwater, due to the difference in environmental characteristics, this puts forward a variety of challenges for scientists to work with IoUT, and one such challenge is the network management with IoUT. This paper gives an overview on (1) underwater network management systems (U-NMS) using acoustic communication in IoUT; (2) the challenges and benefits and use cases of U-NMS; (3) fault, configuration, accounting, performance, security and constrained management (FCAPSC) functionalities of U-NMS and (4) a comparison between network management system in IoT and U-NMS system in IoUT. Additionally, this paper shows the prototype design and implementation setup of U-NMS in a laboratory environment, using lightweight machine to machine (LWM2M) and acoustic communication technology for IoUT. This paper will contribute much to the profit of researchers and industry players in uncovering the critical areas of the Internet of Underwater Things.