Object counting in aquaculture is an important task, and has been widely applied in fish population estimation, estimation of lobster abundance and scallop stocks, and so forth. However, underwater object counting is challenging for biologists and marine scientists because of the diversity of backgrounds of the lake or ocean, the uncertainty of the object motion, and the occlusion between objects. With the rapid development of sensor, computer vision, and acoustic technologies, advanced and efficient counting methods are available in aquaculture. We reviewed underwater object counting methods in aquaculture, provided a survey including more than 50 articles in the recent 10 years, and analyzed the pros and cons of the counting methods and the applicable scenarios of those methods. Finally, the major challenges and future trends of underwater object counting in aquaculture are discussed.