Abstrakt:  We will present work in progress concerning the classification of Calabi-Yau threefolds in P^6. We shall begin with a general introduction by showing general properties of these threefolds. Then we shall discuss the relationship between known constructions of such Calabi--Yau threefolds and the constructions of projected del Pezzo
surfaces in P^5. Finally we will present the classification of Calabi-Yau threefolds contained in five dimensional quadrics of arbitrary rank and the resulting classification of Calabi-Yau threefolds of degree 12, 13 and 14 in P^6.

This is joint work with G. Kapustka.