  The basic workings of inflationary models are summarized, along with the
arguments that strongly suggest that our universe is the product of inflation.
I describe the quantum origin of density perturbations, giving a heuristic
derivation of the scale invariance of the spectrum and the leading corrections
to scale invariance. 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. 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. 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.
