  We consider the leading twist $T$-odd contributions as the dominant source of
the azimuthal and transverse single spin asymmetries in SIDIS and dilepton
production in Drell-Yan Scattering. These asymmetries contain information on
the distribution of quark transverse spin in (un)polarized protons. In the
spectator framework we estimate these asymmetries at HERMES kinematics and at
$50\ {\rm GeV}$ for the proposed experiments at GSI, where an anti-proton beam
is ideal for studying the transversity properties of quarks due to the
dominance of {\em valence} quark effects.
