  Our understanding of the elasticity and rheology of disordered materials,
such as granular piles, foams, emulsions or dense suspensions relies on
improving experimental tools to characterize their behaviour at the particle
scale. While 2D observations are now routinely carried out in laboratories, 3D
measurements remain a challenge. In this paper, we use a simple model system, a
packing of soft elastic spheres, to illustrate the capability of X-ray
microtomography to characterise the internal structure and local behaviour of
granular systems. Image analysis techniques can resolve grain positions, shapes
and contact areas; this is used to investigate the material's microstructure
and its evolution upon strain. In addition to morphological measurements, we
develop a technique to quantify contact forces and estimate the internal stress
tensor. As will be illustrated in this paper, this opens the door to a broad
array of static and dynamical measurements in 3D disordered systems
