  The basic workings of inflationary models are summarized, along with 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. To clarify (but not
resolve) this ambiguity, a toy model of an eternally inflating universe is
introduced. Vilenkin's proposal for avoiding these problems is also discussed,
as is the question of whether it is meaningful to discuss probabilities for
unrepeatable measurements.
