Aquaculture is a complex, multicomponent, interactive process that is dependent on water resource, animal, human as well as capital investment. The measured data affected by complicated environmental factors are usually nonlinear and various, which make it difficult to accurately control system. Traditional machine learning methods have not satisfied the actual requirements because these models can’t extract intrinsic features of data. As an important branch of machine learning, deep learning has been emphasized in both academia and industry due to the specialty of automatic feature extraction from raw data. Accordingly, application of deep learning in aquaculture is expected to produce promising results. Quite a number of researches have highlighted its potential for detection, classification, counting and prediction tasks in aquaculture. Here, we review application of deep learning in aquaculture, and categorize research by aquatic products (i.e. fish, shrimp, scallop, coral, jellyfish, aquatic macroinvertebrates, phytoplankton and water quality), presenting examples of current research in each object. The studies involve fish classification, fish counting, fish behavior monitoring, fish fillets defect detection, shrimp disease research, shrimp freshness detection, pearl classification, scallops counting, coral species classification, activity monitoring of cold water coral polyps, jellyfish detection, aquatic macroinvertebrates classification, phytoplankton classification, trend prediction of red tide biomass, dissolved oxygen content prediction, chlorophyll-a content prediction, temperature prediction, marine floating raft aquaculture monitoring, obstacle avoidance in underwater environments and virtual fish grasp. We found that deep learning technique achieved higher accuracy and efficiency than other methods in most studies. In addition, advantages and limitations of deep learning in aquaculture were discussed, with recommendation on future research directions and challenges. We hope that this review will provide valuable insights to advance aquaculture in future research.