  The status of different extensions of the Random Phase Approximation (RPA) is
reviewed. The general framework is given within the Equation of Motion Method
and the equivalent Green's function approach for the so-called Self-Consistent
RPA (SCRPA). The role of the Pauli principle is analyzed. A comparison among
various approaches to include Pauli correlations, in particular, renormalized
RPA (r-RPA), is performed. The thermodynamic properties of nuclear matter are
studied with several cluster approximations for the self-energy of the
single-particle Dyson equation. More particle RPA's are shortly discussed with
a particular attention to the alpha-particle condensate. Results obtained
concerning the Three-level Lipkin, Hubbard and Picket Fence Models,
respectively, are outlined. Extended second RPA (ESRPA) is presented.
