Human　brain　effective　connectivity　characterizes　the　causal　effects　of　neural　activities　among　different　brain　regions.　Studies　of　brain　effective　connectivity　networks　(ECNs)　for　different　populations　contribute　significantly　to　the　understanding　of　the　pathological　mechanism　associated　with　neuropsychiatric　diseases　and　facilitate　finding　new　brain　network　imaging　markers　for　the　early　diagnosis　and　evaluation　for　the　treatment　of　cerebral　diseases.　A　deeper　understanding　of　brain　ECNs　also　greatly　promotes　brain-inspired　artificial　intelligence　(AI)　research　in　the　context　of　brain-like　neural　networks　and　machine　learning.　Thus,　how　to　picture　and　grasp　deeper　features　of　brain　ECNs　from　functional　magnetic　resonance　imaging　(fMRI)　data　is　currently　an　important　and　active　research　area　of　the　human　brain　connectome.　In　this　survey,　we　first　show　some　typical　applications　and　analyze　existing　challenging　problems　in　learning　brain　ECNs　from　fMRI　data.　Second,　we　give　a　taxonomy　of　ECN　learning　methods　from　the　perspective　of　computational　science　and　describe　some　representative　methods　in　each　category.　Third,　we　summarize　commonly　used　evaluation　metrics　and　conduct　a　performance　comparison　of　several　typical　algorithms　both　on　simulated　and　real　datasets.　Finally,　we　present　the　prospects　and　references　for　researchers　engaged　in　learning　ECNs.