  We investigate the possibility of gravity localization on the brane in the
context of supersymmetric theories. To realize this scenario one needs to find
a theory with the supersymmetric flow stable in IR at two critical points, one
with positive and the other with negative values of the superpotential. We
perform a general study of the supersymmetric flow equations of gauged massless
supergravity interacting with arbitrary number of vector multiplets and
demonstrate that localization of gravity does not occur. The same conclusion
remains true when tensor multiplets are included. We analyze all recent
attempts to find a BPS brane-world and conclude that localization of gravity on
the brane in supersymmetric theories remains a challenging but unsolved
problem.
