Gram-negative bacteria are intrinsically resistant to many antibiotics. Species that have acquired multidrug resistance and cause infections that are effectively untreatable present a serious threat to public health. The problem is broadly recognized and tackled at both the fundamental and applied levels. This paper summarizes current advances in understanding the molecular bases of the low permeability barrier of Gram-negative pathogens, which is the major obstacle in discovery and development of antibiotics effective against such pathogens. Gaps in knowledge and specific strategies to break this barrier and to achieve potent activities against difficult Gram-negative bacteria are also discussed.