Clavulanic acid is a potent β-lactamase inhibitor produced by Streptomyces clavuligerus, widely used in combination with β-lactam antibiotics to combat antimicrobial resistance. This systematic review analyzes the most successful methodologies for clavulanic acid overproduction, focusing on the highest yields reported in bench-scale and bioreactor-scale fermentations. Studies have demonstrated that glycerol is the preferred carbon source for clavulanic acid production over other sources like starch and dextrins. The optimization of feeding strategies, especially in fed-batch operations, has improved glycerol utilization and extended the clavulanic acid production phase. Organic nitrogen sources, particularly soybean protein isolates and amino acid supplements such as L-arginine, L-threonine, and L-glutamate, have been proven effective at increasing CA yields both in batch and fed-batch cultures, especially when balanced with appropriate carbon sources. Strain engineering approaches, including mutagenesis and targeted genetic modifications, have allowed for the obtainment of overproducer S. clavuligerus strains. Specifically, engineering efforts that overexpress key regulatory genes such as ccaR and claR, or that disrupt competing pathways, redirect the metabolic flux towards CA biosynthesis, leading to high clavulanic acid titers. The fed-batch operation at the bioreactor scale emerges as the most feasible alternative for prolonged clavulanic acid production with both wild-type and mutant strains, allowing for the attainment of high titers during cultivations.