  This talk, which was presented at Stephen Hawking's 60th birthday conference,
begins with a discussion of the early development of the theory of inflationary
density perturbations. Stephen played a crucial role in this work, at every
level. Much of the foundation for this work was laid by Stephen's 1966 paper on
cosmological density perturbations, and by his 1977 paper with Gary Gibbons on
quantum field theory in de Sitter space. Stephen was a major participant in the
new work, and he was also a co-organizer of the 1982 Nuffield Workshop, where
divergent ideas about inflationary density perturbations were thrashed about
until a consensus emerged. In the second part of the talk I summarize the
recent observational successes of these predictions, I present a graph of the
probability distribution for the time of last scattering for CMB photons, and I
summarize a recent theorem by Borde, Vilenkin, and me which shows that although
inflation is generically eternal to the future, an inflationary region of
spacetime must be incomplete in null and timelike past directions.
