Carbon, and particularly graphite in its various forms, is an attractive electrode material. Two areas of particular interest are modified carbon electrodes and carbon nanotube electrodes. In this article we focus on the relationship between surface structure and electrochemical and chemical reactivity of electrodes based on these materials. We overview recent work in this area which has led us to believe that much of the catalytic activity, electron transfer and chemical reactivity of graphitic carbon electrodes is at surface defect sites, and in particular edge-plane-like defect sites. We also question the claimed special "catalytic" properties of carbon nanotube modified electrodes.