  We review the Weyl-Wigner formulation of quantum mechanics in phase space. We
discuss the concept of Narcowich-Wigner spectrum and use it to state necessary
and sufficient conditions for a phase space function to be a Wigner
distribution. Based on this formalism we analize the modifications introduced
by the presence of boundaries. Finally, we discuss the concept of
environment-induced decoherence in the context of the Weyl-Wigner approach.
