The use of artificial intelligence (AI) has increased since the middle of the 20th century, as evidenced by its applications to a wide range of engineering and science problems. Air traffic management (ATM) is becoming increasingly automated and autonomous, making it lucrative for AI applications. This paper presents a systematic review of studies that employ AI techniques for improving ATM capability. A brief account of the history, structure, and advantages of these methods is provided, followed by the description of their applications to several representative ATM tasks, such as air traffic services (ATS), airspace management (AM), air traffic flow management (ATFM), and flight operations (FO). The major contribution of the current review is the professional survey of the AI application to ATM alongside with the description of their specific advantages: (i) these methods provide alternative approaches to conventional physical modeling techniques, (ii) these methods do not require knowing relevant internal system parameters, (iii) these methods are computationally more efficient, and (iv) these methods offer compact solutions to multivariable problems. In addition, this review offers a fresh outlook on future research. One is providing a clear rationale for the model type and structure selection for a given ATM mission. Another is to understand what makes a specific architecture or algorithm effective for a given ATM mission. These are among the most important issues that will continue to attract the attention of the AI research community and ATM work teams in the future.