Three studies were conducted to facilitate the design and synthesis of new, more efficient inhibitors of β-lactamase enzymes. A series of C6-substituted penicillin sulfones were synthesized and evaluated against class A and C β-lactamases. Results indicate a hydrogen-bonding donating group at the β-face of the molecule improves inhibitory activity, and steric bulk at C6 greatly decreases activity against class A β-lactamases. The hydroxymethyl at C6 had significant inhibitory activity against all serine-based β-lactamases and exceeds commercially available inhibitors. Computer-assisted docking studies, performed by Dr. Buynak, suggest that the 6β-hydroxymethyl substituent of the inhibitor may function as a hydrogen-bond donor, similar to the N-H of the 6β-acylamino substituent of the natural penicillins, thus facilitating recognition of the inhibitor and acylation of the β-lactamase. Mass spectrometric studies, performed by Dr. Robert A. Bonomo, show that water is eliminated from the hydroxymethyl substituent subsequent to acylation of the β-lactamase, prospectively leading to an acyl-enzyme with enhanced hydrolytic stability. The second and third studies focused on the development of synthetic routes leading to the preparation of key intermediates in the synthesis of new antibiotics and β-lactamase inhibitors, including molecules which are predicted to have superior properties to presently available compounds. An efficient and general synthesis of allenyl sulfides was developed by reaction of thioaryl copper (I) complexes with propargylic mesylates. These allenes were subsequently lithiated and reacted with a series of carbon, silicon, tin, and sulfur-derived electrophiles, leading to the preparation of a diverse library of substituted allenyl sulfides. Lastly, the allenyl stannyl sulfides were shown to participate in Stille coupling reactions with selected vinyl iodides, leading to a general route to the synthetically challenging, and potentially useful vinyl allenes. Some of the resultant substituted allenes were shown to react with chlorosulfonyl isocyanate to produce densely functional α-alkylidene-β-lactams. Such substituted β-lactams possess utility in the synthesis of new antibiotics and β-lactamase inhibitors.