With　the　rapid　development　of　modern　computers,　the　numerical　method　has　been　widely　used　in　engineering.　The　finite　element　method(FEM),　one　of　the　most　popular　methods,　has　been　successfully　integrated　into　many　commercial　software　packages.　However,　there　are　still　some　limitations　in　the　current　FEM,　including　the　modeling　of　dynamic　response　of　unbounded　domain,　the　representation　of　stress　singularities,　and　the　automatic　mesh　generation.　Additional　challenges　are　posed　by　the　emerging　data　formats　used　in　modern　geometric　modeling　techniques,　such　as　digital　image,　stereolithography(STL)models,　and　point　cloud　models.　The　scaled　boundary　finite　element　method(SBFEM)is　a　novel　semi-analytical　method　combining　some　of　the　advantages　of　FEM　and　boundary　element　method(BEM).　It　only　discretizes　the　boundary　of　the　element,　while　the　radial　direction　is　solved　analytically,　reducing　the　spatial　dimension　by　one.　As　a　result,　the　SBFEM　is　perfectly　suitable　for　the　modelling　of　dynamic　stiffness　of　unbounded　domain　and　representing　stress　singularities.　Furthermore,　it　is　capable　of　modeling　polyhedrons　with　an　arbitrary　number　of　faces　and　nodes,　which　greatly　reduces　the　difficulty　associated　with　mesh　generation　when　combining　with　efficient　octree　algorithm.　Over　the　years,　it　has　been　developed　as　a　general-purpose　numerical　method,　and　a　large　number　of　researchers　have　endeavored　to　apply　the　SBFEM　in　fields　such　as　dynamic　response　of　unbounded　domain,　fracture　mechanics,　nonlinear　analysis,　contact　problem,　adaptive　analysis,　inverse　problem,　and　high　performance　computing.　In　this　article,　the　history　and　latest　progress　in　SBFEM　research　are　systematically　reviewed.　©　2022　Xi＇an　Jiaotong　University.　All　rights　reserved.