Abstract :
The quark transversity distribution is a fundamental but still elusive ingredient of the structure of the nucleon. Its chiral-odd nature makes it difficult to measure. Several experiments all over the world (HERMES at DESY, Hall A and CLAS at Jlab, COMPASS at CERN, STAR and PHENIX at RHIC, BELLE at KEKB, PAX at GSI) are going to provide first results for this observable and for other important and unmeasured pT− dependent distribution and fragmentation functions.