Appears in collection : Arithmetic and Algebraic Geometry: A conference in honor of Ofer Gabber on the occasion of his 60th birthday

We construct toroidal compactifications of the moduli space of Drinfeld modules of rank d with N-level structure. We obtain them as the moduli spaces of log Drinfeld modules of rank d with N-level structure. The theory of toroidal compactifications was announced by Pink long ago (using the works of Fujiwara) but the details are not yet published. We follow the ideas of Pink adding log studies and considering cone decompositions related to simplices of Bruhat-Tits buildings. This is a joint work with T. Fukaya and R. Sharifi.