Cathepsin C is a papain-like cysteine peptidase known primarily for its involvement in the activation of serine peptidases in neutrophils and other immune cells. Its critical role in this process qualifies cathepsin C as a target for the treatment of inflammatory diseases, and its most advanced inhibitor, brensocatib (Insmed), is currently in phase 3 clinical trials for the treatment of non-cystic fibrosis bronchiectasis. Beyond neutrophils, its importance is highlighted by loss-of-function mutations that cause the recessively inherited Papillon-Lefèvre syndrome. At the molecular level, cathepsin C has several structural and functional features that set it apart from other members of the family and enable its selective targeting. It possesses dipeptidyl-peptidase activity (its other common name is dipeptidyl-peptidase I) due to the presence of an additional exclusion domain that also controls its stepwise tetramerization during maturation. In this review article, we summarize the current state of the art regarding the biochemical properties of cathepsin C, its physiological and pathological roles in neutrophils and beyond, and recent advances in the development and evaluation of cathepsin C inhibitors.