The aeronautical networks attract the attention of both industry and academia since Internet access during flights turns to the crucial demand from luxury with the evolving technology. This IFC necessity is currently dominated by the satellite connectivity and A2G network solutions. However, the high installation/equipment cost and latency of the satellite connectivity reduce its efficiency. The A2G networks are utilized through the 4G/5G ground stations deployed on terrestrial areas to solve these satellites’ problems. This terrestrial deployment reduces the coverage area of A2G networks, especially for remote flights over the ocean. The AANETs are designed to provide IFC while solving the primary defects of dominating solutions. The AANET is an entirely novel solution under the vehicular networks since it consists of aircraft with ultra-dynamic and unstructured characteristics. These characteristics separate it from the less dynamic FANETs. Therefore, the environmental and mobility effects cause specific challenges for AANETs. This article presents a holistic review of these open AANET challenges by investigating them in data link, network, and transport layers. Before giving the details of these challenges, this article explores the state-of-the-art literature about satellite and A2G networks for IFC. We then give our specific interest to the AANET by investigating its particular characteristics and open research challenges. The main starting point of this study is that there is a lack of compact research on this exciting topic, although IFC is an inevitable need for the aeronautical industry. Also, the AANET could be underlined by giving all state-of-the-art about the dominating IFC solutions. Therefore, this is the first work exploring the state-of-the-art for all the existing aeronautical networking technologies under a single comprehensive survey by deeply analyzing specific characteristics and open research challenges of AANETs. Additionally, the AANET is a novel topic and should be separately investigated from the FANETs as given in current literature.