  Transverse spin physics is an important part of the scientific programme of
the COMPASS experiment at CERN, which started taking data in 2002, scattering
160 GeV/c muon beam on a polarized $^6$LiD target. The analysis of the data
taken with the target polarized orthogonally to the muon beam direction has
allowed to measure for the first time the Collins and Sivers asymmetries of the
deuteron. Both for the positive and the negative hadrons produced in
semi-inclusive DIS the measured asymmetries are small and, within errors,
compatible with zero: results on part of the accumulated statistics have
already been published. Two-hadron asymmetries and $\Lambda$ polarization
transfered from the struck quark are also being investigated, and preliminary
results on the data collected in the years 2002 and 2003 are given.
