Icing is a frequently encountered phenomenon in aircraft engine operation and poses a direct hazard to flight safety. The development and airworthiness certification of advanced aircraft engines have imposed new requirements on the reliability, precision and cost-effectiveness of icing protection technologies, while also presenting challenges to existing icing research. This paper systematically reviews the progress in the study of aircraft engine icing and its protective methodologies. Focusing on two types of icing-supercooled droplet icing and ice crystal icing-the paper provides a detailed analysis and summary from several key aspects: icing environments and mechanisms, major components susceptible to icing, principal factors influencing icing, as well as computational and experimental research approaches. The technical principles, key technologies and current research status of the mainstream anti-icing and de-icing methods are systematically reviewed. Furthermore, the existing difficulties and challenges are concluded, including the accurate prediction of icing characteristics on rotating surfaces, the formation mechanism and numerical simulation of needle ice, the acquisition of complex cloud evolution and distribution in internal flow passages, the precise prediction of ice crystal and mixed-phase icing, and the high-fidelity experimental simulation and measurement of icing, anti-icing and de-icing processes. Finally, four key directions for future in-depth research are proposed: the icing mechanism and laws of various engine components, the theories and technologies for engine icing, anti-icing and de-icing experimental simulation, high-efficiency and high-fidelity numerical models and methods, as well as ice control strategies based on accurate prediction of icing characteristics. The findings and conclusions presented herein can serve as a reference for ice safety assessment and the advancement of icing protection technologies for advanced aircraft engines.