Understanding the geometry of space and time is an important question both for physics and mathematics. Since the advent of quantum mechanics and relativity, it is a challenge to reconcile the spectral view on space developed in quantum physics with the geometrical description of spacetime in general relativity. Noncommutative geometry is an attempt to overcome this opposition by enlarging the notion of geometry so as to incorporate its spectral nature. The idea of making space noncommutative is probably as old as quantum mechanics, but it has developed considerably since the mid 80’s in various directions, from pure mathematics to theoretical physics, yielding some phenomenological predictions in high energy physics. The aim of this conference is the interplay between noncommutative geometry and physics, notably : • the spectral description of standard model of fundamental interactions and the highlighting of an internal geometry of spacetime; • the introduction of an extended notion of spacetime symmetries, and the consequences for physics; • the proposal of novel frameworks for formulating field theories; • potential new perspectives on the long-standing challenge of finding a quantum theory of gravity.