  We present a critical reappraisal of the available results on the broken
phase of $\lambda(\Phi^4)_4$ theory, as obtained from rigorous formal analyses
and from lattice calculations. All the existing evidence is compatible with
Spontaneous Symmetry Breaking but dictates a trivially free shifted field that
becomes controlled by a quadratic hamiltonian in the continuum limit. As
recently pointed out, this implies that the simple one-loop effective potential
should become effectively exact. Moreover, the usual naive assumption that the
Higgs mass-squared $m^2_h$ is proportional to its ``renormalized''
self-coupling $\lambda_R$ is not valid outside perturbation theory: the
appropriate continuum limit has $m_h$ finite and vanishing $\lambda_R$. A Monte
Carlo lattice computation of the $\lambda(\Phi^4)_4$ effective potential, both
in the single-component and in the O(2)-symmetric cases, is shown to agree very
well with the one-loop prediction. Moreover, its perturbative leading-log
improvement (based on the concept of $\lambda_R$) fails to reproduce the Monte
Carlo data. These results, while supporting in a new fashion the peculiar
``triviality'' of the $\lambda(\Phi^4)_4$ theory, also imply that, outside
perturbation theory, the magnitude of the Higgs mass does not give a measure of
the observable interactions in the scalar sector of the standard model.
