  We present a complete review of the quantum-to-classical limit of open
systems by means of the theory of decoherence and the use of the
Weyl-Wigner-Moyal (WWM) transformation. We show that the analytical extension
of the Hamiltonian provides a set of poles that can be used to (a) explain the
non-unitary evolution of the relevant system and (b) completely define the set
of preferred states that constitute the mixture into which the system
decoheres: the Moving Preferred Basis. Moreover, we show that the WWM of these
states are the best candidates to obtain the trajectories in the classical
phase-space.
