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As the first review in this field, this paper presents an in-depth mathematical view of Intelligent Flight Control Systems (IFCSs), particularly those based on artificial neural networks. The rapid evolution of IFCSs in the last two decades in both the methodological and technical aspects necessitates a comprehensive view of them to better demonstrate the current stage and the crucial remaining steps towards developing a truly intelligent flight management unit. To this end, in this paper, we will provide a detailed mathematical view of Neural Network (NN)-based flight control systems and the challenging problems that still remain. The paper will cover both the model-based and model-free IFCSs. The model-based methods consist of the basic feedback error learning scheme, the pseudocontrol strategy, and the neural backstepping method. Besides, different approaches to analyze the closed-loop stability in IFCSs, their requirements, and their limitations will be discussed in detail. Various supplementary features, which can be integrated with a basic IFCS such as the fault-tolerance capability, the consideration of system constraints, and the combination of NNs with other robust and adaptive elements like disturbance observers, would be covered, as well. On the other hand, concerning model-free flight controllers, both the indirect and direct adaptive control systems including indirect adaptive control using NN-based system identification, the approximate dynamic programming using NN, and the reinforcement learning-based adaptive optimal control will be carefully addressed. Finally, by demonstrating a well-organized view of the current stage in the development of IFCSs, the challenging issues, which are critical to be addressed in the future, are thoroughly identified.