The aim of this review is to present and discuss the most recent literature about the processing of insect biomass and its impact on nutritive value, further implementation of meals and fats derived from invertebrates to livestock (poultry and swine), aquaculture (salmonids), and companion animal diets and their impact on growth performance, metabolic response, and gastrointestinal microbiota shifts. Additionally, the most important barriers to obtaining unified products in terms of their nutritive value are considered, i.e., to define insects' nutrient requirements, including various technological groups and further biomass processing (slaughtering, drying, and storage). Due to the current limitation in the insect production process consisting of the lack of infrastructure, there is stress on the relatively small amount of insect products added to the animal diets as a functional feed additive. Currently, only in the case of pet nutrition may insects be considered a full replacement for commonly used environmentally harmful and allergenic products. Simultaneously, the least information has been published on this topic. Thus, more scientific data are needed, particularly when the pet food branch and insect-based diets are rapidly growing.