Environmental pollution, population increase, water availability and misuse of land are inexorably driving humans to take on important challenges related to sustainability. The next future is expected to see a significant increase of food and feed demands, which determines a serious threat to well-being levels and even survival of modern societies. Within this scenario, the efficient and sustainable use of insects as protein sources has been invoked as a possible strategic solution. As a candidate for remarkable growth, insect farming promises significant benefits to agri-food industry, offering interesting opportunities for implementing circular economy. In the present work, we review selected literature on insect rearing with the aim of providing a short rigorous introduction to the field to researchers, entrepreneurs and common readers. After a general overview of the field, including a description of insect nutritional values, the review focuses on the three insect species that are seemingly set to beneficially affect aquaculture, which is the activity presently more sensitive to circularity and sustainability innovation. Once traditional and advanced insect rearing methods are described, the challenges that the field is going to tackle are suitably highlighted.