Abstract In 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 oski he con jectured that this remains true when we replace the ring of convergent power series by a more general ring This paper presents the state of the art on this problem aimed at non experts In particular we put a slant on the Artin Approximation Problem with con straints