There is no doubt about the strength of the carbon-carbon covalent bond, which coupled with the lightness of the atom, makes it a perfect subject for high strength materials. The initial strength hype over carbon nanotubes (CNT), now being repeated in some circles with graphene, arose from measurements of the strength of individual graphitic layers, and while the scientists were usually (but not always) professionally explicit as to what they had measured, the publicity machines assumed that these figures could also be readily realized in any material made from nanotubes. It is against a background of this overselling that we have watched the gradual improvement in strength of useful materials, especially yarn-like fibres made of carbon nanotubes. Fibres made by the direct spinning process have been used as the subject of this study. If CNT fibres are to displace carbon fibre on a world scale, it will be firstly on the basis of cost, as the direct spinning process for nanotube fibre is eminently scaleable. Secondly, it is the toughness of the fibre which is likely to be one of its major selling points, so while matching existing fibres in tensile properties, it promises to be much more resilient to damage and very much tougher in any case of non-axial loading. Strategies for further development are outlined, as will be the prospects for tuning properties for particular applications. Finally, there will be a personal view as to where it all might be leading.