The present invention provides a method to convert insects or worms into nutrient streams, such as a fat-containing, an aqueous proteinaceous-containing and a solid-containing fraction. The method comprises the steps of: (a) squashing insects or worms thereby obtaining a pulp, (b) subjecting the pulp to enzymatic hydrolysis obtaining thereby a hydrolysed mixture, (c) heating the hydrolysed mixture to a temperature of 70-100° C., and (d) subjecting the mixture to a physical separation step, preferably decanting and/or centrifuging. The fat-containing fraction comprises at least 80 wt. % insect or worm fat of which at least 30 wt. % are saturated fats. The aqueous proteinaceous fraction can be dried to obtain dried proteinaceous material, which contains at least 45 wt. % insect or worm protein-derived matter and at most 25 wt. % insect or worm fat based on dry weight, and has a pepsin digestibility of at least 50%. The resulting nutrient streams can be used in food, feed and pharmaceutical industry.