  A classical result in knot theory says that the Alexander polynomial of a
fibered knot is monic and that its degree equals twice the genus of the knot.
This result has been generalized by various authors to twisted Alexander
polynomials and fibered 3-manifolds. In this paper we show that the conditions
on twisted Alexander polynomials are not only necessary but also sufficient for
a 3-manifold to be fibered. By previous work of the authors this result implies
that if a manifold of the form S^1 x N^3 admits a symplectic structure, then N
fibers over S^1. In fact we will completely determine the symplectic cone of
S^1 x N in terms of the fibered faces of the Thurston norm ball of N.
