  We show that an equivariant vector bundle on a complete toric variety is nef
or ample if and only if its restriction to every invariant curve is nef or
ample, respectively. Furthermore, we show that nef toric vector bundles have a
nonvanishing global section at every point, and deduce that the underlying
vector bundle is trivial if and only if its restriction to every invariant
curve is trivial. We apply our methods and results to study, in particular, the
vector bundles M_L that arise as the kernel of the evaluation map on sections
of L, when L is an ample line bundle. We give examples of twists of such
bundles that are ample but not globally generated.
