  Noncommutative geometry is a mathematical framework that expresses the
structure of space-time in terms of operator algebras. By using the tools of
quantum mechanics to describe the geometry, noncommutative space-times are
expected to give rise to quantum gravity effects, at least in some regime. This
manuscript focuses on the physical aspects of these so-called quantum
space-times, in particular through the formalism of field and gauge theories.
Scalar field theories are shown to possibly trigger mixed divergences in the
infra-red and ultra-violet for the 2-point function at one loop. This
phenomenon is generically called UV/IR mixing and stems from a diverging
behaviour of the propagator. The analysis of such divergences differs from the
commutative case because the momentum space is now also noncommutative. From
another perspective, a gauge theory on $\kappa$-Minkowski, a quantum
deformation of the Minkowski space-time, is derived. A first perturbative
computation is shown to break the gauge invariance, a pathological behaviour
common to other quantum space-times. A causality toy model is also developed on
$\kappa$-Minkowski, in which an analogue of the speed-of-light limit emerges.
The phenomenology of quantum gravity arising from quantum space-times is
discussed, together with the actual constraints it imposes. Finally, a toy
model for noncommutative gravity is tackled, using the former
$\kappa$-Minkowski space-time to describe the tangent space. It necessitates
the notion of noncommutative partition of unity specifically defined there.
