  We explore the Mellin representation of conformal correlation functions
recently proposed by Mack. Examples in the AdS/CFT context reinforce the
analogy between Mellin amplitudes and scattering amplitudes. We conjecture a
simple formula relating the bulk scattering amplitudes to the asymptotic
behavior of Mellin amplitudes and show that previous results on the flat space
limit of AdS follow from our new formula. We find that the Mellin amplitudes
are particularly useful in the case of conformal gauge theories in the planar
limit. In this case, the four point Mellin amplitudes are meromorphic functions
whose poles and their residues are entirely determined by two and three point
functions of single-trace operators. This makes the Mellin amplitudes the ideal
objects to attempt the conformal bootstrap program in higher dimensions.
