Abstract—The integration of Terrestrial Networks (TNs) and Non-Terrestrial Networks (NTNs) is a foundational requirement for Sixth Generation (6G), enabling ubiquitous, resilient, and globally inclusive connectivity. However, existing surveys typically analyze this integration by concentrating on individual dimensions—such as architectural design, control and virtualization mechanisms, or Artificial Intelligence (AI)—while giving limited attention to sustainability considerations. This paper addresses this gap by introducing a unified architecture–AI–sustainability triadic framework, which forms the core contribution of the review. First, the paper provides a structured architectural synthesis that clarifies how different integration models influence the design and operational behavior of TN–NTN systems. Second, it consolidates the role of AI in enabling intelligent, adaptive, and context-aware network operation across integrated space–air–ground environments. Third, it advances sustainability as a primary design principle by synthesizing emerging strategies aimed at improving energy and carbon efficiency in future 6G infrastructures. By examining these three dimensions collectively, the review offers a coherent and comprehensive perspective on TN–NTN convergence, identifies persistent challenges including interoperability limitations and standardization gaps, and outlines future research directions needed to develop resilient, intelligent, and environmentally responsible 6G ecosystems aligned with United Nation Sustainable Development Goals (UN SDGs).