  We evaluate the branching ratio BR($b\rightarrow s,\gamma$) in the minimal
supersymmetric standard model (MSSM), determining the corresponding
phenomenological restrictions on two attractive supergravity scenarios, namely
minimal supergravity and a class of models with a natural solution to the $\mu$
problem. We have included in the calculation some one--loop refinements that
have a substantial impact on the results. The numerical results show some
disagreements with part of the previous results in the literature, while they
are in agreement with others. For minimal supergravity the CLEO upper and lower
bounds put important restrictions on the scalar and gaugino masses in both
cases $\mu<0$ and $\mu>0$. For the other supergravity scenarios the relevant
CLEO bound is the upper one. It is stressed the fact that an eventual
improvement of the experimental bounds of order $10^{-4}$ would strengthen the
restrictions on the MSSM dramatically. This would be enough to discard these
supergravity scenarios with $\mu<0$ if no discrepancy is found with the
standard model prediction, while for $\mu>0$ there will remain low-energy
windows.
