Unveiling the physical conditions around black holes is one of the major astrophysical challenges of the 21st century. Indeed we are still at the dawn of black hole astrophysics and very little about these objects is understood: what are the geometry, dynamics and energetics of the accretion flow onto the black hole? How can accretion of material onto the hole be simultaneously intimately related to violent relativistic ejecta and/or powerful self-confined persistent jets? What are the processes at the origin of the fascinating hysteresis cycles observed in some X ray binaries? These unsolved and puzzling issues are at the heart of this ANR2012-CHAOS proposal. It is focused on Black-Hole X-ray Binaries (hereafter BHB ) as they are actually the best candidates for such studies, their complex multi-wavelength behaviour occurring on timescales that can be handled very well (i.e. minutes to months). This project is the natural development of a precedent theoretical and numerical ANR “Jeunes Chercheurs” with now the additional ambition of getting closer to observations, in spite of the major criticism made upon our ANR 2011 submission. Indeed, collaborating with experts in multi-wavelength observations is crucial for the present project for two reasons. First, a precise knowledge of the global observational characteristics of microquasars is needed to drive the theoretical and numerical developments. Such knowledge is unaccessible for non-experts. Second, a direct comparison with observations is essential to validate/invalidate our theoretical framework. Within the present project, each field of expertise (dynamics, radiation, observation) will first improve existing tools and/or develop new ones: (i) time dependent accretion disc models, where ejection is consistently taken into account, will be designed; (ii) multi-zones, radiative and kinetic simulation codes will be developed and (iii) the most up-to-date broad band (from radio to gamma-rays) database of BHB properties will be set-up, coupled with opening of new observing windows. Then, these tools will be brought together in an unprecedented effort within the community. Thus, besides the development of new simulation tools that can be applied to many different astrophysical problems, we will be able to produce synthetic Spectral Energy Distribution for these sources, analyse and predict their timing evolution, and directly compare with the most complete and stringent set of multi-wavelength data that we will produce. By gathering together well-known experts in observation, radiation processes and theory of accretion-ejection processes around compact objects, this project aims at strengthening the French BHB community. It will not only strengthen our leadership in the field but will also significantly enhance our knowledge on the accretion-ejection processes in BHB and, more generally, in all types of compact accretors.