One-dimensional　dynamic　nonlinear　constitutive　relation　of　soil　is　the　key　to　numerical　method　and　dynamic　response　of　site　and　foundation.　Firstly,　the　development　and　research　advancement　are　reviewed　and　summarized.　Then,　the　central　problemg,　which　are　analysis　methods,　application　rules　from　equal　amplitude　cyclic　load　process　to　irregular　load,　equivalent　methods　of　test　hysteretic　damping,　curve　shapes　of　hysteretic　constitutive　etc.　are　analyzed.　The　advantages　and　disadvantages　of　the　models　are　compared　with　each　other,　and　the　current　research　results　are　introduced　especially.　Finally,　existing　problems　are　pointed　out　and　the　problems,　which　need　to　be　studied　in　future,　are　suggested.