Abstract: Deligne's logarithmic comparison theorem and the degeneracy of the spectural sequence of logarithmic de Rham complex gives the mixed Hodge structure of a projective smooth variety with a normal crossing boundary divisor. In this talk, we will try to build a similar theory on toroidal embeddings. In particular, we will show the E_1-degeneracy of the spectral sequence of the logarithmic de Rham complex of any toroidal triple. This gives a geometric proof of a more general version of Danilov's conjecture.