The rapid evolution of wireless communication has affected unmanned aerial vehicles (UAV), which are expected to be used in diverse applications in smart cities, military operations, and cellular networks. To address the significant impacts of rapid wireless communication advancements, along with the escalating demand for user equipment (UE), multiple access technique approaches, such as non-orthogonal multiple access (NOMA), have been proposed. NOMA has the key distinguishing feature of supporting more UE, particularly UAV-enabled communication networks. In these networks, to support more UE, multiple UE share the same frequency resources, which can be beneficial for UAV communication networks. To achieve optimal results, UAVs need to adaptively adjust to their environment, and this can be achieved through employing machine learning (ML). ML is a subfield of artificial intelligence (AI) that enables computers to learn from data and make predictions or decisions without being explicitly programmed. Employing ML can aid NOMA for UAV networks to analyze various parameters and rely on accurate predictions regarding various aspects of communication, such as channel conditions, user mobility, and traffic demands. The use of ML in NOMA-UAV networks can lead to significant improvements in wireless communication systems. In this paper, we present a survey on the potential of NOMA techniques applied to UAVs using ML methods to enhance UAVs in wireless communication networks. Specifically, a basic overview of UAV and NOMA will first be introduced. The role of NOMA in UAV networks is then divided into two categories: the principles and applications of NOMA in UAV networks. Finally, implement ML on NOMA for UAVs by representing the diverse applications of ML systems. In addition, we highlight several open research problems as possible directions for future research.INDEX TERMS Aerial networks, machine learning (ML), non-orthogonal multiple Access (NOMA), unmanned aerial vehicles (UAV).