Antimicrobial drug resistance is a growing threat to global public health. Multidrug resistance among the 'ESKAPE' organisms - encompassing Enterococcus faecium, Staphylococcus aureus, Klebsiella pneumoniae, Acinetobacter baumannii, Pseudomonas aeruginosa and Enterobacter spp. - is of particular concern because they are responsible for many serious infections in hospitals. Although some promising agents are in the pipeline, there is an urgent need for new antibiotic scaffolds. However, antibacterial researchers have struggled to identify new small molecules with meaningful cellular activity, especially those effective against multidrug-resistant Gram-negative pathogens. This difficulty ultimately stems from an incomplete understanding of efflux systems and compound permeation through bacterial membranes. This Opinion article describes findings from target-based and phenotypic screening efforts carried out at AstraZeneca over the past decade, discusses some of the subsequent chemistry challenges and concludes with a description of new approaches comprising a combination of computational modelling and advanced biological tools which may pave the way towards the discovery of new antibacterial agents.