Review of COMPASS results on transverse-spin effects in SIDIS

The transversity parton distribution remains a poorly known cornerstone in the nucleon spin structure. While the Collins effect in spin asymmetries in Semi-Inclusive DIS (SIDIS) is one crucial tool to address the transversity function, the most promising alternative is the azimuthal asymmetry in SIDIS when a hadron pair is detected in the final state. In this case, the chiral-odd transversity function is coupled to another chiral-odd function, i.e. the hadron-pair interference fragmentation function (IFF). The measurement of azimuthal asymmetries in hadron-pair production on a transversely polarised nucleon target has been performed at COMPASS using a 160 GeV/c muon beam of CERN's M2 beam line. Results from the 2007 and 2010 recent measurements will be presented and compared to model predictions.