QCD evolution of transversity in leading and next-to-leading order

I shall present. a rather pedagogical discussion of the transversity distributions in the quark-parton model and, in particular, the role of perturbative QCD corrections. Among the topics I shall discuss are: LO and NLO evolution, the Soffer bound and so-called K factors in the Drell-Yan process. The main conclusion will be that, compared to unpolarised or even longitudinally polarised hadron scattering, the case of transverse spin should actually provide a far clearer window onto the workings of QCD and the interplay with the quark-parton model.