Abstract: Higher torsion invariants generalize the notion of the classical Reidemeister torsion. While the Reidemeister torsion is a tool for distinguishing between finite CW-complexes that are homotopy equivalent but not homeomorphic, higher torsion can detect bundles of smooth compact manifolds that are fiberwise homotopy equivalent (or even fiberwise homeomorphic), but have different smooth structures. In recent years various constructions of higher torsion invariants appeared including the higher analytical torsion of Bismut and Lott and Morse-theoretical construction of Igusa and Klein. The talk will present a construction of higher torsion that is based on the machinery of homotopy theory and some of its applications. The talk is based on joint work with W. Dorabiala, J. Klein and B. Williams.