Similar to terrestrial networks, underwater wireless networks (UWNs) also aid several critical tasks including coastal surveillance, underwater pollution detection, and other maritime applications. Currently, once underwater sensor nodes are deployed at different levels of the sea, it is nearly impossible or very expensive to reconfigure the hardware, for example, battery. Taking this issue into account, considerable amount of research has been carried out to ensure minimum energy costs and reliable communication between underwater nodes and base stations. As a result, several different network protocols were proposed for UWN, including MAC, PHY, transport, and routing. Recently, a new paradigm was introduced claiming that the intermittent nature of acoustic channel and signal resulted in designing delay tolerant routing schemes for the UWN, known as an underwater delay tolerant network. In this paper, we provide a comprehensive survey of underwater routing protocols with emphasis on the limitations, challenges, and future open issues in the context of delay tolerant network routing.