  In 1938, Stueckelberg introduced a scalar field which makes an Abelian gauge
theory massive but preserves gauge invariance. The Stueckelberg mechanism is
the introduction of new fields to reveal a symmetry of a gauge--fixed theory.
We first review the Stueckelberg mechanism in the massive Abelian gauge theory.
  We then extend this idea to the standard model, stueckelberging the
hypercharge U(1) and thus giving a mass to the physical photon. This introduces
an infrared regulator for the photon in the standard electroweak theory, along
with a modification of the weak mixing angle accompanied by a plethora of new
effects. Notably, neutrinos couple to the photon and charged leptons have also
a pseudo-vector coupling. Finally, we review the historical influence of
Stueckelberg's 1938 idea, which led to applications in many areas not
anticipated by the author, such as strings. We describe the numerous proposals
to generalize the Stueckelberg trick to the non-Abelian case with the aim to
find alternatives to the standard model. Nevertheless, the Higgs mechanism in
spontaneous symmetry breaking remains the only presently known way to give
masses to non-Abelian vector fields in a renormalizable and unitary theory.
