<p>World aquaculture has demonstrated stable growth in production volumes for the last three decades. The competitiveness of the aquaculture market is growing steadily and the amount of data that fish-farmers have to manage is rapidly increasing. Mathematical modeling is the key factor in improving the fish farming industry and switching from experience-based to knowledge-based precision aquaculture. In this context, mathematical models are crucial tools for sustainable development. This paper presents a review of the literature on mathematical modeling in aquaculture. Using the scientific web search engine Google Scholar, we discovered 154 characteristic research papers considering mathematical models. We perform manual summarizing and classification of the papers by aquaculture problem, scale of the models, and methods used, and develop a classification. In total, we discovered mathematical models related to twenty different aquaculture problems and four scales, from cage/pool-wide to region-wide. We also describe the mathematical methods most commonly used and demonstrate examples of which specific mathematical methods are applied to solve aquaculture problems.</p>