Underwater wireless sensor network (UWSN) is a new technolog that can be used for various purposes, including ocean tracking and underwater exploration, military surveillance, disaster management, industrial applications, and scientific research. These applications require the sensed data to be routed to the destination, and this results in making the data routing one of the essential parts in designing such applications. High propagation delay, restricted bandwidth, 3D deployment, and energy constraints are some of the challenges that UWSN faces when developing routing protocols. Therefore, to mitigate these challenges, efficient routing protocols are proposed according to the specific application. This paper surveys recently routing protocols for UWSN. Furthermore, each routing protocol's main idea and essential operation are presented and its merits and demerits. There are two types of routing protocols surveyed: location-based and location-free routing protocols. Each type is divided into two sub-categories: those that take into account node mobility and those that do not. The surveyed protocols are evaluated through the analytical method in which these protocols are compared through a wide range of parameters like packet delivery ratio, end-to-end delay, energy efficiency, and reliability. Some of the surveyed protocols are evaluated through the numerical simulation method by using Aqua-Sim with NS2.30 and are compared through packet delivery ratio, end-to-end delay, and energy consumption. This survey’s core goal is to encourage more research into improving UWSN routing protocols for better underwater exploration and monitoring.