OXA-48-type β-lactamases are now routinely encountered in bacterial infections caused by carbapenem-resistant Enterobacterales. These enzymes are of high and growing clinical significance due to the importance of carbapenems in treatment of healthcare-associated infections by Gram-negative bacteria, the wide and increasing dissemination of OXA-48 enzymes on plasmids, and the challenges posed by their detection. OXA-48 confers resistance to penicillin (which is efficiently hydrolyzed) and carbapenem antibiotics (more slowly broken down). In addition to the parent enzyme, a growing array of variants of OXA-48 is now emerging. The spectrum of activity of these variants varies, with some hydrolyzing expanded-spectrum oxyimino-cephalosporins. The growth in importance and diversity of the OXA-48 group has motivated increasing numbers of studies that aim to elucidate the relationship between structure and specificity and establish the mechanistic basis for β-lactam turnover in this enzyme family. In this review we collate recently published structural, kinetic, and mechanistic information on the interactions between clinically relevant β-lactam antibiotics and inhibitors with OXA-48 β-lactamases. Collectively, these studies are starting to form a detailed picture of the underlying bases for the differences in β-lactam specificity between OXA-48 variants, and the consequent differences in resistance phenotype. We focus specifically on aspects of carbapenemase and cephalosporinase activities of OXA-48 β-lactamases and discuss β-lactamase inhibitor development in this context. Throughout the review, we also outline key open research questions for future investigation.