Aquaculture systems can benefit from the recent development of advanced control strategies to reduce operating costs and fish loss and increase growth production efficiency, resulting in fish welfare and health. Monitoring the water quality and controlling feeding are fundamental elements of balancing fish productivity and shaping the fish growth process. Currently, most fish-feeding processes are conducted manually in different phases and rely on time-consuming and challenging artificial discrimination. The feeding control approach influences fish growth and breeding through the feed conversion rate; hence, controlling these feeding parameters is crucial for enhancing fish welfare and minimizing general fishery costs. The high concentration of environmental factors, such as a high ammonia concentration and pH, affect the water quality and fish survival. Therefore, there is a critical need to develop control strategies to determine optimal, efficient, and reliable feeding processes and monitor water quality. This paper reviews the main control design techniques for fish growth in aquaculture systems, namely algorithms that optimize the feeding and water quality of a dynamic fish growth process. Specifically, we review model-based control approaches and model-free reinforcement learning strategies to optimize the growth and survival of the fish or track a desired reference live-weight growth trajectory. The model-free framework uses an approximate fish growth dynamic model and does not satisfy constraints. We discuss how model-based approaches can support a reinforcement learning framework to efficiently handle constraint satisfaction and find better trajectories and policies from value-based reinforcement learning.