The　brain　effective　connectivity　networks　characterize　the　causal　interactions　of　neural　activity　between　brain　regions.　Researches　on　brain　effective　connectivity　networks　of　different　populations　can　not　only　provide　a　new　perspective　for　understanding　the　pathological　mechanism　of　neuropsychiatric　diseases,　but　also　provide　novel　brain　network　imaging　markers　for　the　early　diagnosis　and　evaluation　for　treatment　of　diseases,　thus　have　very　important　theoretical　and　practical　value.　Using　computational　approaches　to　identify　brain　effective　connectivity　networks　from　functional　magnetic　resonance　imaging　(fMRI)　data　is　currently　an　important　subject　in　the　human　brain　connectome.　This　paper　firstly　summarizes　a　workflow　of　identifying　brain　effective　connectivity　networks　from　fMRI　data　and　illustrates　its　main　processes　and　methods.　Next,　a　comprehensive　category　system　of　identifying　brain　effective　connectivity　networks　is　presented,　and　several　typical　identifying　algorithms　in　each　category　are　described.　Finally,　by　analyzing　challenging　problems　in　this　area,　we　predict　the　further　research　directions　in　identifying　brain　effective　connectivity　networks　and　hope　to　present　some　references　for　related　researches.　Copyright　©　2021　Acta　Automatica　Sinica.　All　rights　reserved.