Air data sensors provide essential measurements to ensure the availability of autopilot and to maintain aircraft performance, flight envelope protection and optimal aerodynamic surfaces control laws. The importance of these sensors imply the existence of embedded fault tolerance features, mainly represented by hardware redundancy. The latter is prone to fail in case of common fault of multiple sensors, especially if the faults are coherent and simultaneous. Increasing the robustness of fault detection and isolation (FDI) techniques for air data sensors to the aforementioned conditions is essential for the development of more autonomous aircraft, reducing crew workload and guaranteeing flight protections under adverse conditions. This paper reviews recent works on Air Data System (ADS) FDI, assessing proposed model, data and signal-driven approaches. We finally argue in favor of data-driven and hybrid approaches for the development of virtual sensors and semi-supervised anomaly detectors, offering an overview of ways forward.