  For a singular Riemannian foliation whose leaves are properly embedded, we
show in the first part of this article the existence of global tubular
neighbourhoods, and we develop a global description of the foliation as
stratification by types of leaves.
  The second part deals with the further restriction to a foliation without
horizontal conjugate points, introduced by Lytchak and Thorbergsson, which in
the special case of an isometric group action equals the concept of
variationally completeness. Therefrom, we deduce a global geometric description
-- the focal points of the leaves are exactly the singular points -- as well as
a topological one: tautness of the leaves.
