Underwater acoustic (UWA) channel prediction technology, as an important topic in UWA communication, has played an important role in UWA adaptive communication network and underwater target perception. Although many significant advancements have been achieved in underwater acoustic channel prediction over the years, a comprehensive summary and introduction is still lacking. As the first comprehensive overview of UWA channel prediction, this paper introduces past works and algorithm implementation methods of channel prediction from the perspective of linear, kernel-based, and deep learning approaches. Importantly, based on available at-sea experiment datasets, this paper compares the performance of current primary UWA channel prediction algorithms under a unified system framework, providing researchers with a comprehensive and objective understanding of UWA channel prediction. Finally, it discusses the directions and challenges for future research. The survey finds that linear prediction algorithms are the most widely applied, and deep learning, as the most advanced type of algorithm, has moved this field into a new stage. The experimental results show that the linear algorithms have the lowest computational complexity, and when the training samples are sufficient, deep learning algorithms have the best prediction performance.