Insects are a promising future source of sustainable proteins within a circular economy. Proving the safety of insects for food and feed is necessary prior to supplying them to the market. This literature review provides a state-of-the-art overview of the chemical food safety hazards for insects reared for food and feed, focusing mainly on transfer of contaminants from the substrate. Contaminants covered are: heavy metals, dioxins and polychlorinated biphenyls, polyaromatic hydrocarbons, pesticides, veterinary drugs, mycotoxins, and plant toxins. The twelve insect species reported as having the largest potential as feed and food in the EU are included. Transfer and bioaccumulation of contaminants depend on the chemical, insect species, life stage, and source of contaminant (spiked vs natural), as well as the particular substrate and rearing conditions. The heavy metals lead, arsenic, mercury, and cadmium can accumulate, whereas mycotoxins and polycyclic aromatic hydrocarbons (PAHs) seem not to accumulate. Mycotoxins and veterinary drugs could be degraded by insects; their metabolic routes need to be further investigated. Data are generally limited, but in particular for PAHs, plant toxins, and dioxins and dioxin-like polychlorinated biphenyls. Further research on chemical safety of different edible insects is therefore warranted.