The study of collective behaviour aims to understand how individual-level behaviours can lead to complex group-level patterns. Collective behaviour has primarily been studied in animal groups such as colonies of insects, flocks of birds and schools of fish. Although less studied, collective behaviour also occurs in microorganisms. Here, we argue that slime moulds are powerful model systems for solving several outstanding questions in collective behaviour. In particular, slime mould may hold the key to linking individual-level mechanisms to colony-level behaviours. Using well-established principles of collective animal behaviour as a framework, we discuss the extent to which slime mould collectives are comparable to animal groups, and we highlight some potentially fruitful areas for future research.