The β-lactams retain a central place in the antibacterial armamentarium. In Gram-negative bacteria, β-lactamase enzymes that hydrolyze the amide bond of the four-membered β-lactam ring are the primary resistance mechanism, with multiple enzymes disseminating on mobile genetic elements across opportunistic pathogens such as Enterobacteriaceae (e.g., Escherichia coli) and non-fermenting organisms (e.g., Pseudomonas aeruginosa). β-Lactamases divide into four classes; the active-site serine β-lactamases (classes A, C and D) and the zinc-dependent or metallo-β-lactamases (MBLs; class B). Here we review recent advances in mechanistic understanding of each class, focusing upon how growing numbers of crystal structures, in particular for β-lactam complexes, and methods such as neutron diffraction and molecular simulations, have improved understanding of the biochemistry of β-lactam breakdown. A second focus is β-lactamase interactions with carbapenems, as carbapenem-resistant bacteria are of grave clinical concern and carbapenem-hydrolyzing enzymes such as KPC (class A) NDM (class B) and OXA-48 (class D) are proliferating worldwide. An overview is provided of the changing landscape of β-lactamase inhibitors, exemplified by the introduction to the clinic of combinations of β-lactams with diazabicyclooctanone and cyclic boronate serine β-lactamase inhibitors, and of progress and strategies toward clinically useful MBL inhibitors. Despite the long history of β-lactamase research, we contend that issues including continuing unresolved questions around mechanism; opportunities afforded by new technologies such as serial femtosecond crystallography; the need for new inhibitors, particularly for MBLs; the likely impact of new β-lactam:inhibitor combinations and the continuing clinical importance of β-lactams mean that this remains a rewarding research area.