Green functions play an important role in conformal geometry. In this talk, we shall explain how to compute explicitly the logarithmic singularities of the Green kernels of the conformal powers of the Laplacian, including the Yamabe and Paneitz operators. The results are formulated in terms of explicit conformal invariants arising from the ambient metric of Fefferman-Graham. As applications we obtain a new characterization of locally conformally flat manifolds and a spectral-theoretic characterization of the conformal class of the round sphere.