Light scattering and transport in disordered media has been extensively studied. On the fundamental side, the possibility to study coherent scattering in optics has permitted to address basic issues in mesoscopic physics. On the applied side, methods and techniques have been developed for sensing and imaging in complex media (including biological tissues).

We will present recent results in the theory of light transport (diffusion) and scattering (speckles) that put forward unexpected behaviors. We will discuss an invariance property of the average path length in a wave diffusion process, and the first measurement demonstrating this invariance. In the context of imaging through scattering media, we will show that a spatial correlation between the reflected and transmitted speckles persists even in the multiple scattering regime. This makes possible to quantify the mutual information that connects the transmitted and the reflected light. Finally, we will address the influence of correlations in the disorder on the scattering strength. In the case of hyperuniform materials (a specific class of correlated materials), we will show that disordered materials that are both dense and transparent can be designed. These results bring new perspectives for the design of disordered materials with specific photonic properties, and for the control of light transport in complex media.