  Deligne has conjectured that certain mixed Hodge theoretic invariants of
complex algebraic invariants are motivic. This conjecture specializes to an
algebraic construction of the Jacobian for smooth projective curves, which was
done by A. Weil. The conjecture (and one-motives) are motivated by means of
Jacobians, generalized Jacobians of Rosenlicht, and Serre's generalized
Albanese varieties. We discuss the connections with the Hodge and the
generalized Hodge conjecture. We end with some applications to number theory by
providing partial answers to questions of Serre, Katz and Jannsen.
