  The postulate of universal Weyl conformal symmetry for all elementary
physical fields introduces nonclassical gravitational effects in both conformal
gravitation(CG) and the conformal Higgs model (CHM). The resulting theory is
found to explain major observed phenomena including excessive galactic rotation
velocities and accelerating Hubble expansion, without invoking dark matter
(DM). The recent history of this development is surveyed here. Implications of
the theory include galactic baryonic Tully-Fisher relations and dark galactic
haloes of definite large radius. Cosmological CHM parameters exclude a massive
Higgs boson but are consistent with a novel alternative particle of the
observed mass.
