Consuming insects is a possible alternative to meat consumption that has few detrimental impacts on the environment and human health. Whether novel foods made from insects will become established in Western societies in the coming years depends largely on their acceptance by the respective populations. Numerous studies on the acceptance of insects as a novel food have already been conducted. In this systematic review, the main findings of quantitative, experimental, and tasting studies on the acceptance of insects as a novel food are summarized. The present paper is designed to serve as an orientation for practitioners in the food industry and provides information useful for the design of marketing strategies and target group-oriented product development. In addition, we highlight in which fields future studies could be conducted to further improve the understanding of the acceptance of insects as food in Western societies.