In this work we analyze the development of de Sitter-Fantappie Relativity by analyzing, particularly, its applications to cosmology. The cosmological applications seem to be interesting since they resolve many problems of the standard cosmology. In this scenario the space flatness is linked to the observer geometry and it is independent from the presence and distribution of matter-energy. This resolves the flatness problem without introducing inflationary hypotesis and the global spacetime structure is univocally individuated by the algebraic structure of the physical laws. © 2012 by Nova Science Publishers, Inc. All rights reserved.