The relatively simple Fibre-Bundle geometry of a Yang--Mills gauge theory --- mainly the clear distinction between base and fibre --- made it possible, between 1953 and 1971, to construct a fully quantized version and prove that theory's renormalizability; moreover, nonperturbative (topological) solutions were subsequently found in both the fully symmetric and the spontaneously broken modes (instantons, monopoles). Though originally constructed as a model formalism, it became in 1974 the mathematical mold holding the entire Standard Model (i.e. QCD and the Electroweak theory). On the other hand, between 1974 and 1984, Einstein's theory was shown to be perturbatively nonrenormalizable. Since 1974, the search for Quantum Gravity has therefore provided the main motivation for the construction of Gauge Theories of Gravity. Earlier, however, in 1958-76 several such attempts were initiated, for aesthetic or heuristic reasons, to provide a better understanding of the algebraic structure of GR. A third motivation has come from the interest in Unification, making it necessary to bring GR into a form compatible with an enlargement of the Standard Model. Models can be classified according to the relevant structure group in the fibre. Within the Poincar\'e group, this has been either the R⁴ translations, or the Lorentz group SL(2,C) --- or the entire Poincar\' e SL(2,C)\times R⁴. Enlarging the group has involved the use of the Conformal SU(2,2), the special Affine \overline SA(4,R)=\overline SL(4,R)\times R⁴ or Affine \overline A(4,R) groups. Supergroups have included supersymmetry, i.e. the graded-Poincar\' e group (n=1. . . 8 in its extensions) or the superconformal SU(2,2/n). These supergravity theories have exploited the lessons of the aesthetic-heuristic models --- Einstein--Cartan etc. --- and also achieved the Unification target. Although perturbative renormalizability has been achieved in some models, whether they satisfy unitarity is not known. The nonperturbative Ashtekar program has exploited the understanding of instantons and self-dual solutions in QCD, in the complexification and in the selection of new variables. Note that supergravity involves Lie Derivatives as supertranlations, and several models have treated local spacetime translations similarly. The reduction of the larger groups, down to Poincar\'e, has involved spontaneous fibration and spontaneous symmetry breakdown. In this context, noncommutative geometry may allow for further geometrization.

PACS numbers: 11.15.--q, 04.50.+h