Low consumer acceptance of edible insects and insect-based products is one of the main barriers to the successful implementation of entomophagy in Western countries. This rejection is mainly caused by consumers’ negative emotional responses, psychological/personality traits, and attitudes toward food choices. However, as the role of intrinsic product characteristics on such food choices has not been adequately studied, a systematic review was conducted following the PRISMA method, to analyze studies that have assessed hedonic evaluations, sensory profiling, or emotional responses to edible insects or insect-based products. The majority of studies performed with whole insects and insect flour highlight that insect-based products are more negatively evaluated than control products. Although the sensory properties of insects are affected by species and processing conditions, they are generally negative across sensory dimensions. In particular, insects and insect-based products are generally associated with odor and flavor/taste attributes that are related to old/spoiled food. These negative attributes can be linked to the fat fraction of edible insects, with insect oils being very negatively evaluated by consumers. On the other hand, defatted fractions and deodorized oils are not associated with these negative attributes, further supporting the hypothesis that the fat fraction is responsible for the negative odor and flavor/taste attributes. However, there is still a lack of studies assessing the sensory profile of edible insects and insect-based products, as well as consumers’ emotional responses to their consumption. Future studies should focus on the effects of different processing conditions, products incorporating insect fractions (namely protein concentrates/isolates and defatted fractions), and evaluation by target consumer groups.