  We describe the "islands of inversion" that occur when approaching the
neutron drip line around the magic numbers N=20, N=28 and N=40 in the framework
of the Interacting Shell Model in very large valence spaces. We explain these
configuration inversions (and the associated shape transitions) as the result
of the competition between the spherical mean field (monopole) which favors
magicity and the correlations (multipole) which favor deformed intruder states.
We also show that the N=20 and N=28 islands are in reallity a single one, which
for the Magnesium isotopes is limited by N=18 and N=32.
