Bacterial resistance is a continuously evolving threat to our most common antibiotics; the β-lactams. Most recently, the production of β-lactamase enzymes by bacteria rendered many of our current antibiotics unusable threatening to plunge us into a ‘pre-antibiotic’ era. Metallo-β-lactamases (MBLs) play a key role in bacterial resistance to β-lactam antibiotics by efficiently catalysing the hydrolysis of the β-lactam amide bond. Since their discovery, the clinically relevant MBLs, Verona integrin-encoded metallo-β-lactamase (VIM-2), Imipenemase (IMP-1), New Delhi metallo-β-lactamase (NDM-1) and Sao Paulo metallo-β-lactamase (SPM-1), have spread across the world with cases reported in almost all countries. This thesis describes a number of approaches to the identification of inhibitors of MBLs. A combination of structure-based drug design, chemical synthesis and biological evaluation has been used to rationally identify novel inhibitors of VIM-2, IMP-1, NDM-1 and SPM-1 which have also been co administered with a current β-lactam antibiotic and been found to re-sensitise the bacteria to the antibiotic. Four novel classes of inhibitor have been investigated by taking different approaches to inhibitor discovery. A vHTS screening campaign was conducted to identify potential inhibitors from libraries of known compounds. The campaign identified some weak binding inhibitors. Boronic acid-based inhibitors were identified by using vHTS and de novo design respectively and were synthesised which gave IC50’s in the region of 10 nM against VIM-2 and NDM-1. Additionally, a new computational method for the identification of peptides which bind to enzymes has been developed which found Pro-Cys-Phe to be the most active peptide for binding to NDM-1 with an IC50 of 183 µM. This method could be applied to many other systems. In the final approach, de novo design using SPROUT led to the design of a novel thiol based inhibitor class. The inhibitor class has been co-crystallised in VIM-2 and gives IC50 values in the range of 200 nM. The inhibitor class has also successfully shown a 100 fold recovery of the MIC of meropenem against NDM-1 expressing bacteria.