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Terrestrial networks form the fundamental infrastructure of modern communication systems, serving more than 4 billion users globally. However, terrestrial networks are facing a wide range of challenges, from coverage and reliability to interference and congestion. As the demands of the 6G era are expected to be much higher, it is crucial to address these challenges to ensure a robust and efficient communication infrastructure for the future. To address these problems, Non-terrestrial Network (NTN) has emerged to be a promising solution. NTNs are communication networks that leverage airborne (e.g., unmanned aerial vehicles) and spaceborne vehicles (e.g., satellites) to facilitate ultra-reliable communications and connectivity with high data rates and low latency over expansive regions. This article aims to provide a comprehensive survey on the utilization of network slicing, Artificial Intelligence/Machine Learning (AI/ML), and Open Radio Access Network (ORAN) to address diverse challenges of NTNs from the perspectives of both academia and industry. Particularly, we first provide an in-depth tutorial on NTN and the key enabling technologies including network slicing, AI/ML, and ORAN. Then, we provide a comprehensive survey on how network slicing and AI/ML have been leveraged to overcome the challenges that NTNs are facing. Moreover, we present how ORAN can be utilized for NTNs. Finally, we highlight important challenges, open issues, and future research directions of NTN in the 6G era.