Several species of insects have been observed to perform accurate path integration, constantly updating a vector memory of their location relative to a starting position, which they can use to take a direct return path. Foraging insects such as bees and ants are also able to store and recall the vectors to return to food locations, and to take novel shortcuts between these locations. Other insects, such as dung beetles, are observed to integrate multimodal directional cues in a manner well described by vector addition. All these processes appear to be functions of the Central Complex, a highly conserved and strongly structured circuit in the insect brain. Modelling this circuit, at the single neuron level, suggests it has general capabilities for vector encoding, vector memory, vector addition and vector rotation that can support a wide range of directed and navigational behaviours.