The vast majority of behaviour research focuses on organisms that have brains, yet more than 97% of earth’s taxa are brainless, including large and ecologically significant groups such as the plants, protists, bacteria and fungi. This ‘brainless majority’ face many of the same challenges that have led to sophisticated problem solving abilities in brained animals, yet they must solve problems in the absence of complex cognitive architecture.  In this talk, I will argue that acellular slime moulds are excellent models systems for studying information processing and decision making in brainless organisms. Slime moulds are easy to culture in the lab, and unlike most unicellular organisms, they are easily observable with the naked eye. Despite lacking a brain, slime moulds can solve mazes, make trade-offs between risk and food quality, use a form of ‘externalised’ memory to navigate their environment and make patch-leaving decisions based on the quality of recently consumed food items. Slime moulds are also subject to the same cognitive peculiarities frequently observed in brained animals: these include speed-accuracy trade-offs and violations of economic rationality.   The list of complex behaviours documented in slime moulds continues to grow, yet a clear understanding of how slime moulds manage these problem solving feats in the absence of a brain remains elusive. Nevertheless, these bizarre organisms might hold the key to understanding the evolution of organismal information processing.