A major challenge in the design of composites is to calculate the intensities of the damage mechanisms at any point of a composite structure subjected to complex loading and at any time until final fracture as a result of strain and damage localization. Such final fracture mechanisms always involve delamination and most of the time lead to delamination macrocracks. The huge number of tests carried out on stratified composites in the aerospace industry shows the low level of confidence in models. A significant improvement in this situation, i.e. a drastic reduction in the number of industrial tests, could be achieved if one could create a real synergy among the approaches on different scales which, today, are followed quite independently of one another in the case of laminated composites. Numerous theoretical and experimental works carried out in micromechanics introduce microscale models. An intermediate scale called mesoscale enables one to take into account the mechanisms of damage easily. However, there are only few links between the two scales. The questions discussed here are how to bridge the micro and mesomechanics of laminates and its impact to the micro and meso computational damage modellings for delamination prediction.