The Internet of Underwater Things (IoUT) pertains to a system that utilizes technology of Internet of Things (IoT) for data collection, communication, and control in the underwater environment. The monitoring and management of various parameters in the underwater domain are gathered through the deployment of underwater sensors, communication devices, and controllers. It is crucial in emerging ocean engineering. However, due to the instability of the underwater environment and the particularity of the underwater communication transmission medium, it is vulnerable to security threats, which may damage the system or cause data errors. In this survey, we will discuss the challenges, solutions and future directions of IoUT from security and reliability respectively. In order to ensure the normal operation of IoUT, we analyze the underwater security problems and solutions of the IoUT. Then, we discuss the reliability issue and improved strategies of IoUT system in detail. Finally, we come up with our views about the theories, challenges and future prospects of IoUT security after the comparative analysis.