Graph　neural　network　is　a　powerful　tool　for　solving　various　graph　tasks,　such　as　node　classification　and　graph　classification.　However,　there　is　increasing　evidence　suggesting　that　it　is　sensitive　to　distribution　shifts　and　its　performance　is　reduced　by　at　least　10%　when　distribution　shifts　happen.　In　the　last　three　years,　to　solve　the　wide　existing　distribution　shifts,　some　distribution　robust　strategies　have　been　designed　specifically　for　graph　neural　networks.　It　is　also　one　of　the　popular　research　topics　in　graph　neural　networks　in　recent　years.　Therefore,　in　this　paper,　we　divide　these　strategies　into　three　categories　depending　on　the　specific　problems　they　solve:　distribution　shift　for　semi-supervised　node　classification,　distribution　shift　for　unsupervised　node　classification,　and　out-of-distribution　shift　for　graph　classification.　Furthermore,　we　discuss　and　summarize　the　strategies　for　each　type　of　problem.　After　investigating　these　strategies,　we　put　forward　future　development　direction.　©　2024　The　Authors.