This monograph deals with recent advances in the study of the long-time asymptotics of large solutions to critical nonlinear dispersive equations. The first part of the monograph describes, in the context of the energy critical wave equation, the ''concentration-compactness/rigidity theorem method'' introduced by C. Kenig and F. Merle. This approach has become the canonical method for the study of the ''global regularity and well-posedness'' conjecture...