The heterogeneity of as-synthesized single-walled carbon nanotubes (SWNTs) precludes their widespread application in electronics, optics and sensing. We report on the sorting of carbon nanotubes by diameter, bandgap and electronic type using structure-discriminating surfactants to engineer subtle differences in their buoyant densities. Using the scalable technique of density-gradient ultracentrifugation, we have isolated narrow distributions of SWNTs in which >97% are within a 0.02-nm-diameter range. Furthermore, using competing mixtures of surfactants, we have produced bulk quantities of SWNTs of predominantly a single electronic type. These materials were used to fabricate thin-film electrical devices of networked SWNTs characterized by either metallic or semiconducting behaviour.