Underwater wireless sensor network (UWSN) is currently a hot research field in academia and industry with many underwater applications, such as ocean monitoring, seismic monitoring, environment monitoring, and seabed exploration. However, UWSNs suffer from various limitations and challenges: high ocean interference and noise, high propagation delay, narrow bandwidth, dynamic network topology, and limited battery energy of sensor nodes. The design of routing protocols is one of the solutions to address these issues. A routing protocol can efficiently transfer the data from the source node to the destination node in the network. This article presents a review of underwater routing protocols for UWSNs. We classify the existing underwater routing protocols into three categories: energy-based, data-based, and geographic information-based protocols. In this article, we summarize the underwater routing protocols proposed in recent years. The proposed protocols are described in detail and give advantages and disadvantages. Meanwhile, the performance of different underwater routing protocols is analyzed in detail. Besides, we also present the research challenges and future directions of underwater routing protocols, which can help the researcher better explore in the future.