Based on the study of delaunay triangulation dynamic updating algorithm, this paper reviews the earlier researches about inserting points and constrained edges into an existed Delaunay Triangulation, or deleting points and constrained edges from the Delaunay Triangulation. This paper describes a series of key techniques in detail, such as point location, LOP principle, diagonal exchanging etc., and also compares the advantages and disadvantages of these algorithms, furthermore analyses the solved problems and existing problems. Finally the problems existing in the delaunay triangulation dynamic updating algorithms are summarized, and some suggestions about future work are proposed in the end.