  We discuss geometrical aspects of Higgs systems and Toda field theory in the
framework of the theory of vector bundles on Riemann surfaces of genus greater
than one. We point out how Toda fields can be considered as equivalent to Higgs
systems -- a connection on a vector bundle $E$ together with an
End($E$)--valued one form both in the standard and in the Conformal Affine
case. We discuss how variations of Hodge structures can arise in such a
framework and determine holomorphic embeddings of Riemann surfaces into locally
homogeneous spaces, thus giving hints to possible realizations of
$W_n$--geometries. }
