  After a rapid introduction to the physical motivations and a succinct
presentation of heuristic results, this survey summarises the main mathematical
results known on the Edwards-Anderson and the Sherrington-Kirkpatrick models of
spin glasses. Although not complete proofs but rather sketches of the relevant
steps and important ideas are given, only results for which complete proofs are
known --- and for which the author has been able to reproduce all the
intermediate logical steps --- are presented in the sections entitled
`mathematical results'. This paper is intended to both physicists, interested
to know which articles among the multitude of papers published on the subject
go beyond the heuristic arguments to obtain rigorous irrefutable results, but
also to the mathematicians, interested in finding out how rich is the physical
intuitive way of thinking and in being inspired by the heuristic results in
view of a mathematical rigorisation. An extended, but not exhaustive,
bibliography is included.
