  We clarify the way in which cosmological perturbations of quantum origin,
produced during inflation, assume classical properties. Two features play an
important role in this process: First, the dynamics of fluctuations which are
presently on large cosmological scales leads to a very peculiar state (highly
squeezed) that is indistinguishable, in a precise sense, from a classical
stochastic process. This holds for almost all initial quantum states. Second,
the process of decoherence by interaction with the environment distinguishes
the field amplitude basis as a robust pointer basis. We discuss in detail the
interplay between these features and use simple analogies such as the free
quantum particle to illustrate the main conceptual issues.
