Bacterial multidrug efflux transporters have distinct molecular features and mechanisms that enable their impressive substrate polyspecificity. These transporters are involved in all physiological processes where nonspecific but active transport across membranes is critical for survival and proliferation. Importantly, efflux pumps contribute to bacterial virulence and pathogenesis, as well as the spread of antibiotic resistance in clinics. Transporters belonging to several protein superfamilies have been selected for polyspecificity by evolution and augmented with accessory proteins that extend and couple transport reactions across the inner and outer membranes of the bacterium. As a result, bacteria are equipped with diverse efflux machines that protect cells from a broad variety of toxic compounds including antibiotics and other small molecule therapeutics. The inhibition of such polyspecific biomolecular machines is a challenging task, which still awaits an efficient solution. Here, we review the molecular mechanisms of efflux pumps from Gram-negative bacteria and recent advances and challenges associated with the discovery of effective inhibitors of these pumps.