  The investigation of transverse spin and transverse momentum effects in deep
inelastic scattering is one of the key physics programs of the COMPASS
collaboration. Three channels have been analyzed at COMPASS to access the
transversity distribution function: The azimuthal distribution of single
hadrons, involving the Collins fragmentation function, the azimuthal dependence
of the plane containing hadron pairs, involving the two-hadron interference
fragmentation function, and the measurement of the transverse polarization of
Lambda hyperons in the final state. Azimuthal asymmetries in unpolarized
semi-inclusive deep-inelastic scattering give important information on the
inner structure of the nucleon as well, and can be used to estimate both the
quark transverse momentum k_T in an unpolarized nucleon and to access the
so-far unmeasured Boer-Mulders function. COMPASS has measured these asymmetries
using spin-averaged 6LiD data.
