The XVth International Workshop on Numerical Methods for Non-Newtonian Flows (XVth IWNMNNF-2007) was held on the island of Rhodes, Greece, together with the 5th meeting of the Hellenic Society of Rheology, in June 6-10, 2007. Since their inception in 1979, in Providence, Rhode Island, USA, the workshops are rotated biennially between North America and Europe. This was the first time the meeting was held in Greece.