The research of arcuate structure about its geometry，kinematics，classification，main research methods and controlling factors has been comprehensively reviewed. The results are as follows: (1) According to its interior structural trendline distribution and interrelation in plane view, the arcuate structure is classified as parallel，convergence，divergence，truncation and disorder type; (2) The geometrykinematics classification is more practical to use and worth while attention; (3) Palaeomagnetism、strain analysis、modeling and sedimentology are main methods used in the research of arcuate structure; (4)The main controlling factor of arcuate structure includes the basin prototype，foreland basement uplift，continental boundary，strikeslip faults，regional decollement，rigid indentor and multiple structural superimposition; (5) The typical arcuate structures in China include the northeastern part of Tibet plateau，southern Tianshan，Xuqian arc and Xuefengshan and so on, but the kinematics and dynamics research about those arcuate structures are still weak. At present, the 3D strain analysis and mechanism are still weak, which will be the important topics in the future. 