Edible insects are characterized by their low environmental footprint compared with traditional sources of animal and plant proteins. This is due to the high feed conversion efficiency of edible insects. The black soldier fly (Hermetia illucens) larvae (BSFL) are one of the preferred candidates to be used as alternative sources of protein, due to their ability to add value to a wide range of organic and food waste streams. The ability of BSFL to convert organic matter into protein has resulted in a viable and sustainable ingredient to be utilized in animal feed or human food. BSFL have also been considered as key components of the circular economy due to their intrinsic characteristics and properties. The evaluation of the chemical composition, nutritive value, and functional properties of BSFL have been achieved by the utilization of traditional methods of analysis, although most of these procedures do not agree with the requirements of a circular economy due to their intrinsic characteristics (e.g., destructive, energy use, highly reactive reagents, etc.). Therefore, green analytical technologies have been evaluated, of which infrared (IR) spectroscopy has several advantages. This article reviews current and potential applications of IR spectroscopy combined with chemometrics to analyze the proximate composition, functional characteristics, and traceability of BSFL and frass samples.