The global production of cultured crustaceans for 2018 is predicted to be ~8.63 million tonnes, and shrimp represents a significant portion of cultured crustaceans. Demands for shrimp are raising, also in developing countries as consumer preferences have evolved with rising incomes. Shrimp is mainly produced for consumption but during processing economically valuable products are being generated such as chitosan, which is used in cosmetics, food and beverages, agrochemicals and pharmaceuticals. However, the potential and sustainability of shrimp aquaculture production currently suffer from high mortality rates, losses due to especially bacterial and viral infections, and hence suboptimal yields. Vibrio parahaemolyticus acute hepatopancreatic necrosis and white spot syndrome virus (WSSV) disease outbreaks are examples of economically devastating disease outbreaks in shrimp. There is a need for prophylaxis of infectious diseases and for finding novel strategies for conditioning economically important shrimp broods so that they can produce more robust progenies and develop tolerance against biotic (pathogens) and abiotic stressors. Training the innate immune system of shrimp could be a possible avenue for improving animal’s health, and it might serve as potential unique strategy for conditioning the brood stock to have more robust progenies. The current review provides an overview on innate immune responses in shrimp after exposure to bacteria, viruses and abiotic stressors and on the possibilities to train the innate immune system of shrimp in order to improve health, not only of the animal itself but also of its progeny.