  We continue our study of F-thresholds begun in math/0607660 by an in depth
analysis of the hypersurface case. We use the D--module theoretic description
of generalized test ideals which allows us to show that in any F--finite
regular ring the F-thresholds of hypersurfaces are discrete and rational (in
math/0607660 the finite type over a field case was shown for arbitrary ideals).
Furthermore we show that any limit of F-pure thresholds of principal ideals in
bouneded dimension is again an F-pure-threshold, hence in particular the limit
is rational. The study of the set of F-pure-thresholds leads to natural analogs
of conjectures of Shokurov and Koll\'{a}r (for log canonical thresholds) in the
case of F-pure-thresholds.
