  Single spin asymmetries in semi-inclusive deep-inelastic scattering off
transversely polarized nucleon targets have been under intense experimental
investigation over the past few years. They provide new insights into QCD and
the nucleon structure. For instance, they allow the determination of the third
yet-unknown leading-twist quark distribution function $\Delta_{T}q(x)$, the
transversity distribution. Additionally, they give insight into the parton
transverse momentum distribution and angular momentum.
  The measurement of transverse spin effects in semi-inclusive deep-inelastic
scattering is an important part of the COMPASS physics program. In the years
2002-2004 data were collected scattering a 160 GeV muon beam on a transversely
polarized deuteron target. In 2007, additional data were collected on a
transversely polarized proton target. New results from the analysis of the
proton data will be presented. A different but not less important insight into
the nucleon structure might be given by the Sivers asymmetry. This angular
dependence of the cross-section arises from an intrinsic asymmetry in the
parton transverse momentum distribution. The Sivers function is tightly related
to the total angular momentum carried by the quarks in the nucleon. New COMPASS
results for the Sivers asymmetry of the proton will be shown.
