Abstract:  Deligne showed that the rational cohomology of every complex algebraic variety (possibly singular and/or non-compact) carries a remarkable structure: the weight filtration. This filtration expresses the way in which the cohomology of any variety is related to cohomologies of smooth projective ones.  In this talk, I will review the properties of Deligne's weight filtration by means of simple examples. Then, I will explain analogous results within the context of rational homotopy, focusing on the applications to the topology of singular complex varieties.