Recent research in underwater wireless sensor networks (UWSNs) has gained the attention of researchers in academia and industry for a number of applications. They include disaster and earthquake prediction, water quality and environment monitoring, leakage and mine detection, military surveillance and underwater navigation. However, the aquatic medium is associated with a number of limitations and challenges: long multipath delay, high interference and noise, harsh environment, low bandwidth and limited battery life of the sensor nodes. These challenges demand research techniques and strategies to be overcome in an efficient and effective fashion. The design of routing protocols for UWSNs is one of the promising solutions to cope with these challenges. This paper presents a survey of the routing protocols for UWSNs. For the ease of description, the addressed routing protocols are classified into two groups: localization-based and localization-free protocols. These groups are further subdivided according to the problems they address or the major parameters they consider during routing. Unlike the existing surveys, this survey considers only the latest and state-of-the-art routing protocols. In addition, every protocol is described in terms of its routing strategy and the problem it addresses and solves. The merit(s) of each protocol is (are) highlighted along with the cost. A description of the protocols in this fashion has a number of advantages for researchers, as compared to the existing surveys. Firstly, the description of the routing strategy of each protocol makes its routing operation easily understandable. Secondly, the demerit(s) of a protocol provides (provide) insight into overcoming its flaw(s) in future investigation. This, in turn, leads to the foundation of new protocols that are more intelligent, robust and efficient with respect to the desired parameters. Thirdly, a protocol can be selected for the appropriate application based on its described merit(s). Finally, open challenges and research directions are presented for future investigation.