Antibiotic resistance has become the most significant threat to human health across the globe. Polymyxins are often used as the only available therapeutic option against Gram-negative â€˜superbugsâ€™, namely Acinetobacter baumannii, Pseudomonas aeruginosa and Klebsiella pneumoniae. The limited pharmacological and clinical knowledge on the polymyxins in the old literature substantially limited optimizing their clinical use. The current chapter provides a general introduction to this first-ever polymyxin book which comprehensively reviews the significant progress over the last two decades in the chemistry, microbiology, pharmacology, clinical use and drug discovery of polymyxins. In particular, recent pharmacological results have led to the first scientifically-based dosing recommendations and facilitated the discovery of new-generation polymyxins. Future challenges in polymyxin research are highlighted, aiming at improving the clinical utility of this last-line defence.