  I briefly review the advancements in the construction of the graviton
propagator in the context of LQG and Spinfoam Models. In particular the
problems of the Barrett-Crane vertex in giving the correct long-distance limit
and the introduction of the new corrected models. This kind of calculation
applied to an alternative vertex with given asymptotic can give the correct
propagator and is then able to help selecting spinfoam models. In particular
the study of the asymptotic properties of the new models shows the predicted
behavior able to overcome the BC difficulties and to give the correct
propagator
