Carbon nanotubes have been applied in several areas of nerve tissue engineering to probe and augment cell behaviour, to label and track subcellular components, and to study the growth and organization of neural networks. Recent reports show that nanotubes can sustain and promote neuronal electrical activity in networks of cultured cells, but the ways in which they affect cellular function are still poorly understood. Here, we show, using single-cell electrophysiology techniques, electron microscopy analysis and theoretical modelling, that nanotubes improve the responsiveness of neurons by forming tight contacts with the cell membranes that might favour electrical shortcuts between the proximal and distal compartments of the neuron. We propose the ‘electrotonic hypothesis’ to explain the physical interactions between the cell and nanotube, and the mechanisms of how carbon nanotubes might affect the collective electrical activity of cultured neuronal networks. These considerations offer a perspective that would allow us to predict or engineer interactions between neurons and carbon nanotubes.