Electrically conductive composites that contain conductive filler dispersed in an insulating polymer matrix are usually prepared by the vigorous mixing of the components. This affects the structure of the filler particles and thereby the properties of the composite. It is shown that by careful mixing nano-scale features on the surface of the filler particles can be retained. The fillers used possess sharp surface protrusions similar to the tips used in scanning tunnelling. microscopy. The electric field strength at these tips is very large and results in field assisted (Fowler-Nordheim) tunnelling. In addition the polymer matrix intimately coats the filler particles and the particles do not come into direct physical contact. This prevents the formation of chains of filler particles in close contact as the filler content increases. In consequence the composite has an extremely high resistance even at filler loadings above the expected percolation threshold. The retention of filler particle morphology and the presence of an insulating polymer layer between them endow the composite with a number of unusual properties. These are presented here together with appropriate physical models.