Despite its major role in economic growth and development, the agriculture sector is facing many challenges globally. More significant problems have been continuously induced over the years, such as desertification, lack of infrastructure over vast agriculture areas, environmental pollution, excessive use of pesticides, lack of water resources, land fertility decline, and many more. As a solution, the idea of smart agriculture started pervading the world with the ability of transforming traditional farming sector to modern automated one for better crop field management. This can be done by using the technology of Wireless Sensor Networks (WSNs) where diverse agriculture sensors are located on the ground to measure different crop field parameters. However, as the number of sensor nodes increases as the difficulty in managing the system network increases. Consequently, common limitations are to be considered such as energy management, communication interruption, bad connectivity, and difficulties in nodes localization. Therefore, the idea of using Unmanned Aerial Vehicle (UAV) along with WSN in smart agriculture becomes cruicial to improve the system capabilities. UAVs can help locate and identify sensors on the ground, ensure a correct delivery of data, and assist in every stage of the crop field cycle. With its ability to provide better solution for crop fields management, UAV grabbed researchers' attention and encouraged them to deeply study this area and try to develop innovative UAV-WSN based applications that can be integrated with the agriculture sector. Hence, it is important to study UAV in all its aspects as it becomes the heart of the smart agriculture system. This article focuses particularly on UAV's type and mathematical model selection. Therefore, to understand UAV's functionality, this paper surveys different mathematical modelling techniques to derive the UAV plant, examines parameters identification methods to numerically evaluate the model, and discusses existing UAV open-source simulators to verify the ability of the selected model in realistic scenarios. Furthermore, key challenges and future research directions are presented to continuously improve the WSN-UAV based applications in smart agriculture.