  We review the theoretical foundations and most important physical
applications of the Pinch Technique (PT). This method allows the construction
of off-shell Green's functions in non-Abelian gauge theories that are
independent of the gauge-fixing parameter and satisfy ghost-free Ward
identities. We first present the diagrammatic formulation of the technique in
QCD, deriving at one loop the gauge independent gluon self-energy, quark-gluon
vertex, and three-gluon vertex, together with their Abelian Ward identities.
The generalization to theories with spontaneous symmetry breaking is carried
out in detail, and the connection with the optical theorem and the dispersion
relations are explained within the electroweak sector of the Standard Model.
The equivalence between the PT and the Feynman gauge of the Background Field
Method (BFM) is elaborated, and the crucial differences between the two methods
are critically scrutinized. The Batalin-Vilkovisky quantization method and the
general formalism of algebraic renormalization are introduced, and the
all-order generalization of the PT is thoroughly examined. The extension of the
PT to the non-perturbative domain of the QCD Schwinger-Dyson equations is
presented systematically, and the main advantages of the resulting
self-consistent truncation scheme are discussed. A plethora of physical
applications relying on the PT are reviewed, such as the definition of
gauge-independent off-shell form-factors, the construction of non-Abelian
effective charges, the gauge-invariant treatment of resonant transition
amplitudes and unstable particles, and the dynamical generation of an effective
gluon mass.
