  We give an equivalent description of taut submanifolds of complete Riemannian
manifolds as exactly those submanifolds whose normal exponential map has the
property that every preimage of a point is a union of submanifolds. It turns
out that every taut submanifold is also $\mathbb Z_2$-taut. We explicitely
construct generalized Bott-Samelson cycles for the critical points of the
energy functionals on the path spaces of a taut submanifold which, generically,
represent a basis for the $\mathbb Z_2$-cohomology. We also consider singular
Riemannian foliations all of whose leaves are taut. Using our characterization
of taut submanifolds, we are able to show that tautness of a singular
Riemannian foliation is actually a property of the quotient.
