  Relevant physical models are described by singular Lagrangians, so that their
Hamiltonian description is based on the Dirac theory of constraints. The
qualitative aspects of this theory are now understood, in particular the role
of the Shanmugadhasan canonical transformation in the determination of a
canonical basis of Dirac's observables allowing the elimination of gauge
degrees of freedom from the classical description of physical systems. This
programme was initiated by Dirac for the electromagnetic field with charged
fermions. Now Dirac's observables for Yang-Mills theory with fermions (whose
typical application is QCD) have been found in suitable function spaces where
the Gribov ambiguity is absent. Also the ones for the Abelian Higgs model are
known and those for the $SU(2) \times U(1)$ electroweak theory with fermions
are going to be found with the same method working for the Abelian case. The
main task along these lines will now be the search of Dirac's observables for
tetrad gravity in the case of asymptotically flat 3-manifolds. The philosophy
behind this approach is ``first reduce, then quantize": this requires a global
symplectic separation of the physical variables from the gauge ones so that the
role of differential geometry applied to smooth field configurations is
dominating, in contrast with the standard approach of ``first quantizing, then
reducing", where, in the case of gauge field theory, the reduction process
takes place on distributional field configurations, which dominate in quantum
measures. This global separation has been accomplished till now, at least at a
heuristic level, and one is going to have a classical (pseudoclassical for the
fermion) variables basis for the physical description of the $SU(3)\times
SU(2)\times U(1)$ standard model; instead, with tetrad gravity one expects to
