To old and new PDF and PFF

A short review of problems with parton distribution functions in nucleons, non-polarized and polarized, is given. The main part is devoted to the T-odd Collins fragmentation function and to the proton transversity distribution its possible measurements and its first experimental probe via spin asymmetries in semi-inclusive DIS. It is argued that the proton transversity distribution is close to the prediction of chiral quark soliton model could be successfully measured in future DIS experiments with longitudinally polarized target and the Collins analyzing power is linearly growing with z.