A　knowledge　graph　(KG),　also　known　as　a　knowledge　base,　is　a　particular　kind　of　network　structure　in　which　the　node　indicates　entity　and　the　edge　represent　relation.　However,　with　the　explosion　of　network　volume,　the　problem　of　data　sparsity　that　causes　large-scale　KG　systems　to　calculate　and　manage　difficultly　has　become　more　significant.　For　alleviating　the　issue,　knowledge　graph　embedding　is　proposed　to　embed　entities　and　relations　in　a　KG　to　a　low-,　dense　and　continuous　feature　space,　and　endow　the　yield　model　with　abilities　of　knowledge　inference　and　fusion.　In　recent　years,　many　researchers　have　poured　much　attention　in　this　approach,　and　we　will　systematically　introduce　the　existing　state-of-the-art　approaches　and　a　variety　of　applications　that　benefit　from　these　methods　in　this　paper.　In　addition,　we　discuss　future　prospects　for　the　development　of　techniques　and　application　trends.　Specifically,　we　first　introduce　the　embedding　models　that　only　leverage　the　information　of　observed　triplets　in　the　KG.　We　illustrate　the　overall　framework　and　specific　idea　and　compare　the　advantages　and　disadvantages　of　such　approaches.　Next,　we　introduce　the　advanced　models　that　utilize　additional　semantic　information　to　improve　the　performance　of　the　original　methods.　We　divide　the　additional　information　into　two　categories,　including　textual　descriptions　and　relation　paths.　The　extension　approaches　in　each　category　are　described,　following　the　same　classification　criteria　as　those　defined　for　the　triplet　fact-based　models.　We　then　describe　two　experiments　for　comparing　the　performance　of　listed　methods　and　mention　some　broader　domain　tasks　such　as　question　answering,　recommender　systems,　and　so　forth.　Finally,　we　collect　several　hurdles　that　need　to　be　overcome　and　provide　a　few　future　research　directions　for　knowledge　graph　embedding.