Can Transversity Be Measured?

I review the ways that have been proposed to measure the quark transversity distribution in the nucleon. I then explain a proposal, developed by Xuemin Jin, Jian Tang and myself, to measure transversity through the final state interaction between two mesons ($\pi\pi$, $K \bar K$, or $\pi K$) produced in the current fragmentation region in deep inelastic scattering on a transversely polarized nucleon.