Icing on an aircraft is the cause of numerous adverse effects on aerodynamic performance. Although the issue was recognized in the 1920s, the icing problem is still an area of ongoing research due to the complexity of the icing phenomena. This review article aims to summarize current research on aircraft icing in two fundamental topics: icing physics and icing mitigation techniques. The icing physics focuses on fixed wings, rotors, and engines severely impacted by icing. The study of engine icing has recently become focused on ice-crystal icing. Icing mitigation techniques reviewed are based on active, passive, and hybrid methods. The active mitigation techniques include those based on thermal and mechanical methods, which are currently in use on aircraft. The passive mitigation techniques discussed are based on current ongoing studies in chemical coatings. The hybrid mitigation technique is reviewed as a combination of the thermal method (active) and chemical coating (passive) to lower energy consumption.