Chickpeas are inexpensive, protein rich (approximately 20% dry mass) pulses available worldwide whose consumption has been correlated with positive health outcomes. Dietary peptides are important molecules derived from dietary proteins, but a comprehensive analysis of the peptides that can be produced from chickpea proteins is missing in the literature. This review provides information from the past 20 years on the enzymatic production of peptides from chickpea proteins, the reported bioactivities of chickpea protein hydrolysates and peptides, and the potential bitterness of chickpea peptides in food products. Chickpea peptides have been enzymatically produced with pepsin, trypsin, chymotrypsin, alcalase, flavorzyme, and papain either alone or in combination, but the sequences of many of the peptides in chickpea protein hydrolysates remain unknown. In addition, a theoretical hydrolysis of chickpea legumin by stem bromelain and ficin was performed by the authors to highlight the potential use of these enzymes to produce bioactive chickpea peptides. Antioxidant activity, hypocholesterolemic, and angiotensin 1‐converting enzyme inhibition are the most studied bioactivities of chickpea protein hydrolysates and peptides, but anticarcinogenic, antimicrobial, and anti‐inflammatory effects have also been reported for chickpea protein hydrolysates and peptides. Chickpea bioactive peptides are not currently commercialized, but their bitterness could be a major impediment to their incorporation in food products. Use of flavorzyme in the production of chickpea protein hydrolysates has been proposed to decrease their bitterness. Future research should focus on the optimization of chickpea bioactive peptide enzymatic production, studying the bioactivity of chickpea peptides in humans, and systematically analyzing chickpea peptide bitterness.