Lower curvature bounds play an important role in the study of singular spaces. In 2005 Lott, Sturm and Villani presented a synthetic definition in terms of Optimal Transportation of a metric space endowed with a reference measure verifying Ricci curvature greater than K and dimension less than N. By synthetic we mean equivalent to the standard one in the smooth framework but still meaningful for metric measure spaces. This definition is called CD(K,N). We will give a short introduction to CD(K,N) spaces and to some related problems with particular emphasis to the so called local-to-global problem.