  We review some interrelated aspects of thick brane worlds constructed within
the framework of 5D gravity coupled to a scalar field depending on the extra
dimension. It turns out that when analyzing localization of 4D gravity in this
smooth version of the Randall-Sundrum model, a kind of dichotomy emerges. In
the first case the geometry is completely smooth and the spectrum of metric
fluctuations shows a single massless bound state, corresponding to the 4D
graviton, and a tower of massive states described by a continuous spectrum of
Kaluza-Klein excitations starting from zero mass, indicating the lack of a mass
gap. In the second case, there are two bound states, a massless 4D graviton and
a massive excitation, separated by a mass gap from a continuous spectrum of
massive modes; nevertheless, the presence of a mass gap in the graviton
spectrum of the theory is responsible for a naked singularity at the boundaries
(or spatial infinity) of the Riemannian manifold. However, the imposition of
unitary boundary conditions, which is equivalent to eliminating the continuous
spectrum of gravitational massive modes, renders these singularities harmless
from the physical point of view, providing the viability of the model.
