Underwater wireless sensor networks (UWSNs) have recently received a significant amount of attention. Since they have delay/disruption-tolerant networks (DTNs) characteristics, the design of any UWSN scheme must take DTN influences into account, especially in routing protocols. Many researchers have proposed various DTN routing techniques for different types of DTN routing schemes in UWSNs. The authors survey state-of-the-art DTN routing protocols, and use the definition of DTN to classify these proposals into scheduled contact, opportunistic contact and predicted contact. Furthermore, the authors analyse the detailed information in order to draw up a comparison table and also expect to inspire more research into this topic in the future.