  The investigation of transverse spin and transverse momentum effects in deep
inelastic scattering is one of the key physics programs of the COMPASS
collaboration. In the years 2002-2004 COMPASS took data scattering 160 GeV
muons on a transversely polarized 6LiD target. In 2007, a transversely
polarized NH3 target was used. Three different channels to access the
transversity distribution function have been analyzed: 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. Transverse quark
momentum effects in a transversely polarized nucleon have been investigated by
measuring the Sivers distribution function. 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 in an unpolarized nucleon and to access the
so-far unmeasured Boer-Mulders function. COMPASS has measured these asymmetries
using spin-averaged 6LiD data.
