Chickpea (Cicer arietinum L.) is a pulse consumed all over the world, representing a good source of protein, as well as fat, fiber, and other carbohydrates. As a result of the growing global population the demand for the protein component of this pulse is increasing and various approaches have been proposed and developed to extract same. In this review the composition, functionality, and applications of chickpea protein ingredients are described. Moreover, methods to enhance protein quality have been identified, as well as applications of the coproducts resulting from protein extraction and processing. The principal dry and wet protein enrichment approaches, resulting in protein concentrates and isolates, include air classification, alkaline/acid extraction, salt extraction, isoelectric precipitation, and membrane filtration. Chickpea proteins exhibit good functional properties such as solubility, water and oil absorption capacity, emulsifying, foaming, and gelling. During protein enrichment, the functionality of protein can be enhanced in addition to primary processing (e.g., germination and dehulling, fermentation, enzymatic treatments). Different applications of chickpea protein ingredients, and their coproducts, have been identified in research, highlighting the potential of these ingredients for novel product development and improvement of the nutritional profile of existing food products. Formulations to meet consumer needs in terms of healthy and sustainable foods have been investigated in the literature and can be further explored. Future research may be useful to improve applications of the specific coproducts that result from the extraction of chickpea proteins, thereby leading to more sustainable processes.