Complex-shaped structures are commonly seen in industry, and they are high-risk regions of internal defect and even failure during manufacturing and service stages. Ultrasonic non-destructive testing is an effective method to evaluate the manufacturing quality and in-service safety of complex-shaped structures. However, complex surface profile brings challenges to ultrasonic testing, such as difficulties in ultrasonic coupling, surface-conformal scan control, ultrasound incidence and reception, and complex wave propagation behavior. This paper summarizes main research progresses in this field from several aspects, including ultrasonic coupling strategies, transducers, surface conformal scan strategies, surface profile reconstruction, imaging algorithms, and the coupling effects between complex-shaped surface profile and ultrasonic properties of materials. Finally, an outlook on future research trends in ultrasonic imaging of complex-shaped structures is provided, including the testing of three-dimensional structures with ultra-complex irregular surfaces, twodimensional array transducers of high flexibility, and the improvement of ultrasonic imaging algorithms that consider both macro / micro structures and the ultrasonic properties of materials.