The probe of innovative technologies is a furious issue of the day for the improvement of underwater wireless sensor network devices. The undersea is a remarkable and mystical region which is still unexplored and inaccessible on earth. Interest has been increasing in monitoring the medium of underwater for oceanographic data collection, surveillance application, offshore exploration, disaster prevention, commercial, scientific investigation, attack avoidance, and other military purposes. In underwater milieus, the sensor networks face a dangerous situation due to intrinsic water nature. However, significant challenges in this concern are high power consumption of acoustic modem, high propagation latency in data transmission, and dynamic topology of nodes due to wave movements. Routing protocols working in UWSN has low stability period due to increased data flooding which causes nodes to expire quickly due to unnecessary data forwarding and high energy consumption. The quick energy consumption of nodes originates large coverage holes in the core network. To keep sensor nodes functional in an underwater network, dedicated protocols are needed for routing that maintain the path connectivity. The path connectivity consumes more energy, high route updated cost with a high end to end delay for the retransmission of packets. So, in this paper, we are providing a comprehensive survey of different routing protocols employed in UWSN. The UWSN routing protocols are studied and evaluated related to the network environment and quality measures such as the end to end delay, dynamic network topology, energy consumption and packet delivery ratio. The merits and demerits of each routing protocol are also highlighted.