Avibactam, which is the first non-β-lactam β-lactamase inhibitor to be introduced for clinical use, is a broad-spectrum serine β-lactamase inhibitor with activity against class A, class C, and, some, class D β-lactamases. We provide an overview of efforts, which extend to the period soon after the discovery of the penicillins, to develop clinically useful non-β-lactam compounds as antibacterials, and, subsequently, penicillin-binding protein and β-lactamase inhibitors. Like the β-lactam inhibitors, avibactam works via a mechanism involving covalent modification of a catalytically important nucleophilic serine residue. However, unlike the β-lactam inhibitors, avibactam reacts reversibly with its β-lactamase targets. We discuss chemical factors that may account for the apparently special nature of β-lactams and related compounds as antibacterials and β-lactamase inhibitors, including with respect to resistance. Avenues for future research including non-β-lactam antibacterials acting similarly to β-lactams are discussed.