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A curvilinear cylindrical gear is a parallel shaft transmission gear that is not fully marketed. The teeth of this gear transmission have a circular arc curve along the longitudinal direction，it has non-axial force and good lubrication performance. The research status of the curvilinear cylindrical gears is analyzed in detail through a large number of related literatures，the processing methods of the gears，tooth surfaces modeling methods and contact characteristics are expounded. Finally，based on the existing research status，some suggestions for the future research direction of the curvilinear cylindrical gear are put forward.