Asparaginyl endopeptidases (AEPs) are versatile enzymes that in biological systems are involved in producing three different catalytic outcomes for proteins, namely (i) routine cleavage by bond hydrolysis, (ii) peptide maturation, including macrocyclisation by a cleavage-coupled intramolecular transpeptidation and (iii) circular permutation involving separate cleavage and transpeptidation reactions resulting in a major reshuffling of protein sequence. AEPs differ in their preference for cleavage or transpeptidation reactions, catalytic efficiency, and preference for asparagine or aspartate target residues. We look at structural analyses of various AEPs that have laid the groundwork for identifying important determinants of AEP function in recent years, with much of the research impetus arising from the potential biotechnological and pharmaceutical applications.