Curved thin-walled structures are extensively used in many industrial applications including aviation industries. These parts have a specific role in manufacturing of helicopter main rotor blade. Fracture mechanics parameters are needed for life estimation and life extension of curved thin-walled structures. Standard methods of fracture mechanics testing are not applicable to these parts because of curvature and thinness of the specimens. So new test methods for these specimens is necessary to be investigated and developed. Vast trying has been done by scientists to overcome these problems and some theories and experimental methods such as the theory of fracture of thin-walled curved plates, the conventional burst test method and some new non-standard test methods has been initiated and developed. In the present paper, first of all, the theory of thin-walled curved plates has been briefly presented to link the behavior of curved specimens to the flat ones and the conventional burst test (BT) method has been accordingly introduced. Then, the newly developed non-standard test methods such as compact curved tension (CCT), pin loading tension (PLT), three points bending (TPB), double edge notched tension (DENT), internal conical mandrel (ICM) and X-specimen have been reviewed. Finally, a comparison between mentioned methods had been done to determine the most appropriate one.