In the inflationary paradigm, the transition from quantum fluctuations to classical but stochastic density perturbations plays an important role. In particular, it implies that the open quantum system comprising the super-Hubble degrees of freedom can be described with a classical stochastic theory, the “stochastic inflation” formalism. In this framework, the short-wavelength quantum fluctuations act as a classical noise on the dynamics of the super-Hubble scales.