  The possible solution of dark matter problem with neutralinos of
supersymmetric models within the supergravity framework is reviewed. A novel
correlation between the neutralino relic abundance $\Omega_\chi$ and the soft
supersymmetry breaking patterns is demonstrated. It is explained that, this
generic result together with the proton-decay constraint could significantly
reduce the allowed parameter space of the minimal $SU(5)$ supergravity model,
and therefore makes this model more easily testable. The prospect of obtaining
further cosmological constraints from underground experiments for the minimal
$SU(5)$ supergravity model is also briefly discussed.
