  For more than half a century, covariant and differential geometric methods
have been playing a central role in the development of Quantum Field Theory
(QFT). After a brief historic overview of the major scientific achievements
using these methods, we will focus on the covariant and differential geometric
formalism originally proposed by Vilkovisky and DeWitt (VDW). We discuss recent
developments made in addressing the uniqueness of the path-integral measure of
the VDW effective action, and so address the problem of quantum frame
dependence in cosmologically relevant scalar-tensor theories beyond the
classical approximation. Particular attention will be drawn to a long-standing
problem concerning the obstacles that the VDW formalism was facing from its
original conception in describing generic QFTs that include fermions. We show
how in addition to bosons the VDW effective action can be extended to
supermanifolds to include fermions. The so-extended formulation appears to be
very promising for a complete geometrisation of realistic theories of
micro-cosmos, such as the Standard Model and its gravitational sector.
