  We discuss the current picture of the standard model's scalar sector at
strong coupling. We compare the pattern observed in the scalar sector in
perturbation theory up to two-loop with the nonperturbative solution obtained
by a next-to-leading order 1/N expansion. In particular, we analyze two
resonant Higgs scattering processes, ff -> H -> f'f' and ff -> H -> ZZ, WW. We
describe the ingredients of the nonperturbative calculation, such as the
tachyonic regularization, the higher order 1/N intermediate renormalization,
and the numerical methods for evaluating the graphs.
  We discuss briefly the perspectives and usefulness of extending these
nonperturbative methods to other theories.
