Drone deployment has become crucial in a variety of applications, including solutions to traffic issues in metropolitan areas and highways. On the other hand, data collected via drones suffers from several problems, including a wide range of object scales, angle variations, truncation, and occlusion. To process and manipulate visual data from the drones, a variety of image processing algorithms have been employed, each with a distinct aim. Additionally, recent breakthroughs in the field of Artificial Intelligence, particularly deep learning, have attracted broad interest and are being applied to many domains in the framework of smart cities, including road traffic monitoring. The purpose of this study is to conduct a systematic review of drone-based traffic monitoring systems from a deep learning perspective. This work focuses on vehicle detection, tracking, and counting, since they are fundamental building blocks towards founding solutions for traffic congestion, flow rate and vehicle speed estimation. Additionally, drone-based datasets are examined, which face issues and problems caused by the diversity of features inherent of drone devices. The review analysis presented in this work summarizes the literature solutions provided and deployed so far and discusses future research trends in establishing a comprehensive traffic monitoring system in support of the development of smart cities.