  In this paper, we have reviewed the present status of the theory of
equilibrium configurations of compact binary star systems in Newtonian gravity.
Evolutionary processes of compact binary star systems due to gravitational wave
emission can be divided into three stages according to the time scales and
configurations. The evolution is quasi-stationary until a merging process
starts, since the time scale of the orbital change due to gravitational wave
emission is longer than the orbital period. In this stage, equilibrium
sequences can be applied to evolution of compact binary star systems. Along the
equilibrium sequences, there appear several critical states where some
instability sets in or configuration changes drastically. We have discussed
relations among these critical points and have stressed the importance of the
mass overflow as well as the dynamical instability of orbital motions.
Concerning the equilibrium sequences of binary star systems, we have summarized
classical results of incompressible ellipsoidal configurations. Recent results
of compressible binary star systems obtained by the ellipsoidal approximation
and by numerical computations have been shown and discussed. It is important to
note that numerical computational solutions to {\it exact equations} show that
compressibility may lead realistic neutron star binary systems to mass
overflows instead of dynamical disruptions for a wide range of parameters.
