Graph　partitioning　problem,　which　is　one　of　the　most　important　topics　in　graph　theory,　usually　asks　for　a　partition　of　the　vertex　set　of　a　graph　into　pairwise　disjoint　subsets　with　various　requirements.　It　comes　from　the　well-known　Max-Cut　Problem:　Given　a　graph　G,　find　the　maximum　bipartite　subgraph　of　G.　In　practice,　one　often　needs　to　find　a　partition　of　a　given　graph　to　optimize　several　quantities　simultaneously.　Such　problems　are　called　judicious　partition　problems　by　Bollobás　and　Scott.　In　this　survey,　we　present　some　new　results　and　problems　on　graph　partitioning.　©　2022　The　Author(s).　Published　with　license　by　Taylor　&　Francis　Group,　LLC.