  Performing shell model calculations for heavy nuclei is a long-standing
problem in nuclear physics. The shell model truncation in the configuration
space is an unavoidable step. The Projected Shell Model (PSM) truncates the
space under the guidance of the deformed mean-field solutions. This implies
that the PSM uses a novel and efficient way to bridge the two conventional
methods: the deformed mean-field approximations, which are widely applied to
heavy nuclei but able to describe the physics only in the intrinsic frame, and
the spherical shell model diagonalization method, which is most fundamental but
feasible only for small systems. We discuss the basic philosophy in
construction of the PSM (or generally PSM-like) approach. Several examples from
the PSM calculations are presented. Astrophysical applications are emphasized.
