  We discuss a possible explanation of the 25 year old mystery of the large
transverse spin asymmetries found in many semi-inclusive hadron-hadron
reactions. We obtain the first reliable information about the transverse
polarized quark densities Delta_T q(x) and we find surprising implications for
the usual, longitudinal, polarized DIS. The plan of the presentation is as
follows: 1) A brief reminder about the internal structure of the nucleon. 2)
The transverse asymmetries. 3) Why it is so difficult to explain the
asymmetries. 4) Failure and then success using a new soft mechanism. 5)
implications for polarized DIS.
