  In this talk it is reported on an analysis of hard exclusive leptoproduction
of pions within the handbag approach. It is argued that recent measurements of
this process performed by HERMES and CLAS clearly indicate the occurrence of
strong contributions from transversely polarized photons. Within the handbag
approach such gamma*_T -> pi transitions are described by the transversity GPDs
accompanied by twist-3 pion wave functions. It is shown that the handbag
approach leads to results on cross sections and single-spin asymmetries in fair
agreement with experiment. Predictions for other pseudoscalar meson channels
are also briefly discussed.8 pages
