Attempts to relate brain size to behaviour and cognition have rarely integrated information from insects with that from vertebrates. Many insects, however, demonstrate that highly differentiated motor repertoires, extensive social structures and cognition are possible with very small brains, emphasising that we need to understand the neural circuits, not just the size of brain regions, which underlie these feats. Neural network analyses show that cognitive features found in insects, such as numerosity, attention and categorisation-like processes, may require only very limited neuron numbers. Thus, brain size may have less of a relationship with behavioural repertoire and cognitive capacity than generally assumed, prompting the question of what large brains are for. Larger brains are, at least partly, a consequence of larger neurons that are necessary in large animals due to basic biophysical constraints. They also contain greater replication of neuronal circuits, adding precision to sensory processes, detail to perception, more parallel processing and enlarged storage capacity. Yet, these advantages are unlikely to produce the qualitative shifts in behaviour that are often assumed to accompany increased brain size. Instead, modularity and interconnectivity may be more important.