The water source, as a significant body of the earth, with a high value, serves as a hot topic to study Underwater Sensor Networks (UWSNs). Various applications can be realized based on UWSNs. Our paper mainly concentrates on the localization algorithms based on the acoustic communication for UWSNs. An in-depth survey of localization algorithms is provided for UWSNs. We first introduce the acoustic communication, network architecture, and routing technique in UWSNs. The localization algorithms are classified into five aspects, namely, computation algorithm, spatial coverage, range measurement, the state of the nodes and communication between nodes that are different from all other survey papers. Moreover, we collect a lot of pioneering papers, and a comprehensive comparison is made. In addition, some challenges and open issues are raised in our paper.