In the melodies of the Gregorian offertories, the art of the solo singers in the medieval church reached its high point. As if to confirm this position of superiority, a distinct revival of interest in the offertory has been noticeable from the 19th century onwards, not only on the field of scholarly research, but also in practical musical performances. The musical style of the Gregorian offertory inspires description in superlatives. Chant handbooks have always been unanimous about its climactic (but also exceptional) status because of its enormous length, its practically non-formulaic melodic elaboration, its high range - often exceeding the limits of medieval modal theory - its occasional chromaticism, and its highly exceptional treatment of the text. All these features are extremely rare in other chants of the Roman Mass. In many ways the state of today's research stands in sharp contrast to the importance of the topic for our understanding of medieval musical culture. In the autumn of 2004, a symposion at the Centre for Medieval Studies in the Archbishop's Palace, Trondheim, brought together Chant scholars and a Latin philologist from the US, Germany, Italy, Sweden, and Norway to pool present knowledge in this area and to discuss methods and ideas for future research. These well-known experts in the field of the offertory have determined the direction of research in this area during the last fifty years. Research on offertories reflects the main challenges to modern musicology and philology, from heuristic problems of the many hundred medieval sources to intricate questions of the interpretation of style, function, and Rezeptions-geschichte. Furthermore, as with every Gregorian chant genre, the study of the offertory provides insights not only into the musical history, but also the cultural history of Western society.