  The progress of noncommutative geometry has been crucially influenced, from
the beginning, by quantum physics: we review this development in recent years.
The Standard Model, with its central role for the Dirac operator, led to
several formulations culminating in the concept of a real spectral triple.
String theory then came into contact with NCG, leading to an emphasis on
Moyal-like algebras and formulations of quantum field theory on noncommutative
spaces. Hopf algebras have yielded an unexpected link between the
noncommutative geometry of foliations and perturbative quantum field theory.
The quest for a suitable foundation of quantum gravity continues to promote
fruitful ideas, among them the spectral action principle and the search for a
better understanding of "noncommutative spaces".
