  Sutured manifolds defined by Gabai are useful in the geometrical study of
knots and 3-dimensional manifolds. On the other hand, homology cylinders are in
an important position in the recent theory of homology cobordisms of surfaces
and finite-type invariants. We study a relationship between them by focusing on
sutured manifolds associated with a special class of knots which we call {\it
homologically fibered knots}. Then we use invariants of homology cylinders to
give applications to knot theory such as fibering obstructions, Reidemeister
torsions and handle numbers of homologically fibered knots.
