Although a variety of basic insect behaviours have inspired successful robot implementations, more complex capabilities in these 'simple' animals are often overlooked. By reviewing the general architecture of their nervous systems, we gain insight into how they are able to integrate behaviours, perform pattern recognition, context-dependent learning, and combine many sensory inputs in tasks such as navigation. We review in particular what is known about two specific 'higher' areas in the insect brain, the mushroom bodies and the central complex, and how they are involved in controlling an insect's behaviour. While much of the functional interpretation of this information is still speculative, it nevertheless suggests some promising new approaches to obtaining adaptive behaviour in robots.