  In recent years a lot of attention has been paid to topological spaces which
are a bit more general than smooth manifolds - orbifolds. Orbifolds are
intuitively speaking manifolds with some singularities. The formal definition
is also modelled on that of manifolds, an orbifold is a topological space which
locally is homeomorphic to the orbit space of a finite group acting on $R^n$.
Orbifolds were defined by Satake, as V-manifolds, then studied by W. Thurston,
who introduced the term "orbifold". Due to their importance in physics, and in
particular in the string theory, orbifolds have been drawing more and more
attention. In this paper we propose to show that the classical theory of
geometrical structures, easily translates itself to the context of orbifolds
and is closely related to the theory of foliated geometrical structures, cf.
\cite{Wo0}. Finally, we propose a foliated approach to the study of harmonic
maps between Riemannian orbifolds based on our previous research into
transversely harmonic maps.
