Radii structures with complex geometries are commonly encountered in carbon fiber reinforced plastic (CFRP) composites in aerospace components. How to improve the corresponding nondestructive testing quality on defects is one key issue for the assurance of load-bearing properties. In virtue of numerical modeling and wave propagation analysis, the difficulties of ultrasonic testing in CFRP radii were clarified. Due to the intrinsically elastic anisotropy of CFRP material, the layered structure and the curved surface, the normal incidence of ultrasonic wave could not be easily realized and the wave propagation path kinks seriously. Moreover, the structural noise is obvious and the acoustic coupling is difficult. In view of this problem, the research progress in study of phased array ultrasonic testing (PAUT) was summarized, especially for the radii with a varied cross-section in plate thickness, curvature and included angle. The development of PAUT probe, the ultrasonic imaging based on signal post-processing technique, and the research of solid flexible coupling medium and probe jig were emphasized, respectively. The remaining issues and the future development trend were analyzed.