"Wave propagation in complex (disordered) media stretches our knowledge to the limit in many different fields of physics. It has important applications in seismology, acoustics, radar, and condensed matter. It is a problem of large fundamental interest, notably for the study of Anderson localization.In optics, it is of great importance in photonic devices, such as photonic crystals, plasmonic structures or random lasers. It is also at the heart of many biomedical-imaging issues: scattering ultimately limits the depth and resolution of all imaging techniques.We have recently demonstrated that wavefront shaping –i.e. adaptive optics applied to complex media- is the tool of choice to match and address the huge complexity of this problem in optics. The COMEDIA project aims at developing a novel wavefront shaping toolbox, addressing both spatial and spectral degrees of freedom of light. Thanks to this toolbox, we plan to fulfill the following objectives:1) A full spatiotemporal control of the optical field in a complex environment,2) Breakthrough results in imaging and nano-optics,3) Original answers to some of the most intriguing fundamental questions in mesoscopic physics."