Pseudo-Anosov homeomorphisms of surfaces are characterized by the existence of a pair of transverse foliations whose leaves are stretched/contracted under the homeomorphism. The amount of stretching/contracting is measured by a numerical invariant, which turns out to be an algebraic integer, called the stretch factor. The goal of my talk is to discuss a theorem asserting that all stretch factors are controlled by a certain type of twisted Alexander polynomials of fibered 3-manifolds.