  In 1968, M. Artin proved that any formal power series solution of a system of
analytic equations may be approximated by convergent power series solutions.
Motivated by this result and a similar result of P{\l}oski, he conjectured that
this remains true when the ring of convergent power series is replaced by a
more general kind of ring. This paper presents the state of the art on this
problem, aimed at non-experts.
