Studying autocatalysis - in which molecules catalyse their own formation - might help to explain the emergence of chemical systems that exhibit traits normally associated with biology. When coupled to other processes, autocatalysis can lead to complex systems-level behaviour in apparently simple mixtures. Lipids are an important class of chemicals that appear simple in isolation, but collectively show complex supramolecular and mesoscale dynamics. Here we discuss autocatalytic lipids as a source of extraordinary behaviour such as primitive chemical evolution, chemotaxis, temporally controllable materials and even as supramolecular catalysts for continuous synthesis. We survey the literature since the first examples of lipid autocatalysis and highlight state-of-the-art synthetic systems that emulate life, displaying behaviour such as metabolism and homeostasis, with special consideration for generating structural complexity and out-of-equilibrium models of life. Autocatalytic lipid systems have enormous potential for building complexity from simple components, and connections between physical effects and molecular reactivity are only just beginning to be discovered.
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