Neural circuits govern the interface between the external environment, internal cues and outwardly directed behaviours. To process multiple environmental stimuli and integrate these with internal state requires considerable neural computation. Expansion in neural network size, most readily represented by whole brain size, has historically been linked to behavioural complexity, or the predominance of cognitive behaviours. Yet, it is largely unclear which aspects of circuit variation impact variation in performance. A key question in the field of evolutionary neurobiology is therefore how neural circuits evolve to allow improved behavioural performance or innovation. We discuss this question by first exploring how volumetric changes in brain areas reflect actual neural circuit change. We explore three major axes of neural circuit evolution—replication, restructuring and reconditioning of cells and circuits—and discuss how these could relate to broader phenotypes and behavioural variation. This discussion touches on the relevant uses and limitations of volumetrics, while advocating a more circuit-based view of cognition. We then use this framework to showcase an example from the insect brain, the multi-sensory integration and internal processing that is shared between the mushroom bodies and central complex. We end by identifying future trends in this research area, which promise to advance the field of evolutionary neurobiology.