Unmanned aerial vehicles (UAVs), also known as drones, communicate, collaborate, and form flying ad hoc networks (FANETs) to perform many different missions, ranging from delivery tasks to agriculture applications. Recently, FANETs have been integrated with different technologies, such as artificial intelligence (AI), virtual reality, and Internet of Things. Such new avenues for the use of UAVs directly impact the research on FANETs and cause some major challenges, such as security and physical layer issues, resource management, and UAV positioning issues that need to be addressed. Several researchers have been working for the last few years to propose AI and machine learning (ML)‐based solutions for different use cases in UAV‐based networks. They present the limitations of the existing research work and highlight some possible future works on FANETs. However, exhibiting the trends in the UAV research papers in a quantitative manner is still required to motivate researchers to rethink the research on FANETs. Therefore, this study covers more than 170 scientific publications extracted from five trusted academic databases published from 2013 to 2021 to provide a thorough overview of the main research and development statistics in the area of FANETs, the open challenges existing in this area and the ML‐based solutions to solve these challenges. In addition, the investigation of emerging technologies integrated with FANETs, as well as the simulation tools employed for evaluating FANETs' performance are discussed. Moreover, the future research directions in the area of FANETs are considered within a prospective vision discussion.