In this article we present the physics programs for LHCb and for an e+e− high luminosity asymmetric B factory. Using a few examples, we will show how the measurements which can be performed will allow us to study, in a unique manner, the structure of the New Physics beyond the Standard Model, if discovered at LHC with the general purpose detectors ATLAS and CMS, and/or eventually to extend the domain of the New Physics search to larger energy not accessible at LHC.