High fidelity numerical simulations are conducted to investigate wavy leading edges (WLEs) in transonic flows. In particular the focus is on the mitigation of shock buffet and its radiated noise. The main objective of this work is to give a comprehensive overview of the aerodynamic and aeroacoustic performance of this passive technique previously studied only in subsonic flows. Due to the novelty of this study, a preliminary analysis is conducted slowly varying the incidence angles. This gives information about the aerodynamic performance and the leading edge flow structures. After that, the shock buffet condition is analysed in details focusing first on the unsteady phenomena and then on the radiated noise. The aerodynamic and aeroacoustic performance analyses are conducted including the effect of the WLE amplitude. Finally, a sweep angle is introduced in order to investigate an aeronautical application of this passive technique. Two wavy swept configurations are studied. In the first one, the WLE direction has a sweep angle with respect to the upstream flow, while in the second one, the WLE direction is parallel to the upstream flow. The focus is on the mitigation of shock buffet and the additional unsteady phenomena introduced by the three dimensional configuration. Moreover, the leading edge flow structures are inspected and compared with the unswept case. The study shows that wavy leading edges over supercritical aerofoils represent a promising passive technique to mitigate the shock oscillations and it paves the ground for further studies.