Carbapenem resistance presents a major challenge for the global public health network, as clinical infections caused by carbapenem-resistant organisms (CRO) are frequently associated with significant morbidity and mortality. Ceftazidime–avibactam (CAZ–AVI) is a novel cephalosporin/β-lactamase inhibitor combination offering an important advance in the treatment of CRO infections. CAZ–AVI has been reported to inhibit the activities of Ambler classes A, C, and some class D enzymes. However, bacterial resistance has been emerging shortly after the introduction of this combination in clinical use, with an increasing trend. Understanding these resistance mechanisms is crucial for guiding the development of novel treatments and aiding in the prediction of underlying resistance mechanisms. This review aims to systematically summarize the epidemiology of CAZ–AVI-resistant strains and recently identified resistance mechanisms of CAZ–AVI, with a focus on the production of β-lactamase variants, the hyperexpression of β-lactamases, reduced permeability, and overexpressed efflux pumps. The various mechanisms of CAZ–AVI resistance that have emerged within a short timescale emphasize the need to optimize the use of current agents, as well as the necessity for the surveillance of CAZ–AVI-resistant pathogens.