%0 Journal Article %T New structures on valuations and applications %A Semyon Alesker %J Mathematics %D 2010 %I arXiv %X An overview of some of the recent developments in the theory of valuations on convex sets and its generalizations to manifolds is given. The exposition is focused towards applications to integral geometry; several of such applications are discussed. %U http://arxiv.org/abs/1008.0287v3