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In recent decades, deep learning (DL) has become a rapidly growing research direction, redefining the state-of-the-art performances in a wide range of techniques, such as object detection and speech recognition. In the aircraft design, dynamics, and control field, many works hinge on the information-rich data-driven approach, which includes the fusion-based prognostic and health management, the airliner's flight safety monitoring, intelligent sensing, and flight control systems development. While DL provides great potentials to solve these data-driven problems, a systematic review and discussion as to how the DL has been/can be used for these problems are still missing in relation to the rapidly developing and widely used DL techniques. In this article, we aim to address this urgent issue to provide a timely overview of the state-of-the-art for applying DL to the aircraft design, dynamics, and control field. In particular, we briefly introduce five representative DL methods, i.e., deep neural network, deep autoencoder, deep belief network, convolutional neural network, and recurrent neural network. Mathematical definitions for each method are presented, and illustrative applications are also discussed. We then review the existing DL-based works that have appeared in the aircraft design, dynamics, and control field. The review efforts are divided into two major groups, i.e., the own-ship aircraft modeling, wherein the works have been/can be implemented online for the aircraft design/dynamics/control, and other airplanes research works, wherein DL-based schemes provide offline monitoring of the aircraft operation. We then summarize the data sources and DL architectures. Referring to the experiences of DL research works/techniques development in other related fields, future opportunities, challenges, and potential solutions for implementing DL in the aircraft design, dynamics, and control field are also discussed. [ABSTRACT FROM AUTHOR]