In this talk, I will try to join two recent papers related to the phase transition to Eternal Inflation. In a first part, I will concentrate on slow-roll Inflation, and I will study the phase transition to the eternal regime. I consider the volume of the universe at reheating as order parameter, and I show that there exists a critical value for the classical Inflaton speed, \dot\phi^2/H^4 = 3/(2 \pi^2), where the probability distribution for the reheating volume undergoes a sharp transition. In particular, for sub-critical Inflaton speeds, the system develops a non-vanishing probability of having a strictly infinite reheating volume. In the second part of the talk, I will discuss about a possibility of learning something about Eternal Inflation at LHC. Even if nothing but a light Higgs is observed at the LHC, suggesting that the Standard Model is unmodified up to scales far above the weak scale, Higgs physics can yield surprises of fundamental significance for Cosmology. As has long been known, the Standard Model vacuum may be metastable for low enough Higgs mass, but a specific value of the decay rate holds special significance: for a very narrow window of parameters, our Universe has not yet decayed but the current inflationary period can not be future eternal. Determining whether we are in this window requires exquisite but achievable experimental precision. If the parameters are observed to lie in this special range, particle physics will establish that the future of our Universe is a global big crunch, without harboring pockets of eternal inflation, strongly suggesting that eternal inflation is censored by the fundamental theory.