In this paper the essence of the cell mapping methodology for global analysis of nonlinear dynamical systems is presented. When a nonlinear system is analyzed by this method, the final results can be given in terms of a domain to domain evolution that exhibits the complete dynamic properties of the system in a global fashion. For the paper to serve also as a review article on this methodology, a list of recent publications on cell mapping is included in order to show the range of applications of this new method up to this date.