We clarify the way in which cosmological perturbations of quantum orig
in, produced during inflation, assume classical properties. Two featur
es play an important role in this process: First, the dynamics of fluc
tuations which are presently on large cosmological scales leads to a v
ery peculiar state (highly squeezed) that is indistinguishable, in a p
recise sense, from a classical stochastic process. This holds for almo
st all initial quantum states. Second, the process of decoherence by i
nteraction with the environment distinguishes the field amplitude basi
s as the robust pointer basis. We discuss in detail the interplay betw
een these features and use simple analogies such as the foe quantum pa
rticle to illustrate the main conceptual issues.