Carbon-based nanostructures, such as carbon nanotubes (CNT) and graphene, are used in a range of composite materials and are also being investigated for potential device applications. TEM and SEM provide a wealth of information about the material and their dependence on the processing conditions. This includes the number of walls in CNTs and their diameter, number of sheets in ‘graphene’ (e.g. single layer, bi-layer etc), nature of the carbon bonding (i.e. graphitic or diamond-like bonding?), atomic-scale defects, dispersibility in various solvents etc.