Underwater Wireless Sensor Networks (UWSNs) are finding different applications for offshore exploration and ocean monitoring. In most of these applications, the network consists of significant number of sensor nodes deployed at different depths throughout the area of interest. The sensor nodes located at the sea bed cannot communicate directly with the nodes near the surface level; they require multi-hop communication assisted by appropriate routing scheme. However, this appropriateness depends not only on network resources and application requirements but also on environmental constraints. All these factors provide a platform where a resource-aware routing strategy plays a vital role to fulfill the different application requirements with dynamic environmental conditions. Realizing the fact, significant attention has been given to construct a reliable scheme, and many routing protocols have been proposed in order to provide an efficient route discovery between the sources and the sink. In this paper, we present a review and comparison of different algorithms, proposed recently in order to fulfill this requirement. The main purpose of this study is to address the issues like data forwarding, deployment and localization in UWSNs under different conditions. Later on, all of these are classified into different groups according to their characteristics and functionalities.