With the recent advances in underwater sensor devices and technologies, underwater wireless sensor networks (UWSNs) enable a variety of applications such as underwater exploration and monitoring, disaster prevention, and military surveillance and reconnaissance. However, these kinds of networks faces a number of challenges induced by the nature of the underwater environment and its influence on the physical media. Therefore, new routing protocols are proposed specifically for such networks to mitigate these challenges. This paper surveys some of the recent routing protocols for UWSNs. Specifically, the idea of each protocol is presented as well as its advantages and disadvantages. Furthermore, the presented protocols are classified into different categories. The paper is concluded with some open research issues.