  This paper is a summary of the theory of discrete embeddings introduced in
[5]. A discrete embedding is an algebraic procedure associating a numerical
scheme to a given ordinary differential equation. Lagrangian systems possess a
variational structure called Lagrangian structure. We are specially interested
in the conservation at the discrete level of this Lagrangian structure by
discrete embeddings. We then replace in this framework the variational
integrators developed in [10, Chapter VI.6] and in [12]. Finally, we extend the
notion of discrete embeddings and variational integrators to fractional
Lagrangian systems.
