Although 5G is designed to provide a large range of new digital services such as immersive experiences, connected machines, and Internet of Things (IoT), 5G networks may not be able to completely meet the needs of emerging novel applications, as well as to address the future needs of the business and regulatory ecosystem. Beyond 5G (B5G) and Sixth Generation (6G) wireless systems are expected to overcome 5G network limits and support a broader range of new use cases in this rapidly expanding digital era. In this survey article, we provide a summary of the major 5G networks shortcomings that are discussed in the literature and classify them into a taxonomy of six primary domains. For each of these domains, we also highlight and discuss the research challenges that will be faced in the development of future B5G and 6G networks.