We prove that the knot Floer complex of a fibered knot detects whether the
monodromy of its fibration is right-veering. In particular, this leads to a purely knot Floer theoretic characterization of tight contact structures, by the work of Honda–Kazez–Mati´c.
Our proof makes use of the relationship between the Heegaard Floer homology of mapping
tori and the symplectic Floer homology of area-preserving surface diffeomorphisms. We
describe applications of this work to Dehn surgeries and taut foliations.