  This is an overview of some of the invariants that were discovered by
Welschinger in the context of enumerative real algebraic geometry. Their
definition finds a natural setup in real symplectic geometry. In particular,
they can be studied using techniques from symplectic field theory, of which we
also give a sample. Welschinger invariants are real analogues of certain
Gromov-Witten invariants. This article is an extended set of notes for a talk
at the Bourbaki seminar in April 2011.
