  We report on some general results on the physics of extremal BPS black holes
in four and five dimensions. The duality-invariant entropy-formula for all
$N>2$ extended supergravities is derived. Its relation with the fixed-scalar
condition for the black-hole ``potential energy'' wich extremizes the BPS mass
is obtained. BPS black holes preserving different fractions of supersymmetry
are classified in a U-duality invariant set up. The latter deals with different
orbits of the fundamental representations of the exceptional groups $E_{7(7)}$
and $E_{6(6)}$. We comment upon the interpretation of these results in a string
and M-theory framework.
