  We review the theory of quaternionic Kahler and hyperkahler structures. Then
we consider the tangent bundle of a Riemannian manifold M with a metric
connection D (with torsion) and with its well estabilished canonical complex
structure. With an extra almost Hermitian structure on M it is possible to find
a quaternionic Hermitian structure on TM, which is quaternionic Kahler if, and
only if, D is flat and torsion free. We also review the symplectic nature of
TM. Finally a proper S^3-bundle of complex structures is introduced, expanding
to TM the well known twistor bundle of M.
