  I summarize the arguments that strongly suggest that our universe is the
product of inflation. The mechanisms that lead to eternal inflation in both new
and chaotic models are described. Although the infinity of pocket universes
produced by eternal inflation are unobservable, it is argued that eternal
inflation has real consequences in terms of the way that predictions are
extracted from theoretical models. The ambiguities in defining probabilities in
eternally inflating spacetimes are reviewed, with emphasis on the youngness
paradox that results from a synchronous gauge regularization technique.
Although inflation is generically eternal into the future, it is not eternal
into the past: it can be proven under reasonable assumptions that the inflating
region must be incomplete in past directions, so some physics other than
inflation is needed to describe the past boundary of the inflating region.
