Discovery of the accelerating Universe through Super Novae Ia observation about a decade ago has resulted in a paradigm shift in cosmological research. The present monograph is a consequence of theoretical investigation of dark energy, the agent supposed to be responsible for accelerating the Universe. Two main features of this work are Einstein’s general relativistic approach and time-varying ? models of phenomenological character. It has been possible successfully to match the theoretical models with the observational data regarding the age of the Universe. Observational data of time variation of the gravitational constant G has been considered in the typical phenomenological models. Various time dependent equation of state parameter ? have been used to track the entire evolutionary period of the Universe. Possibility of a two-fluid Universe is also in the purview of this work. Another interesting side of this book is the visualization of the inflationary phase through analytic-graphical method and realization of the role of ? as dark energy in connection to cosmic string. In brief, Einstein’s cosmological constant ? in its new face has resurfaced through this monograph.