<p>The discovery of materials with extreme lattice thermal conductivity (κ_L)—spanning from sub-air thermal insulators to metallic conductors that rival diamond—represents one of the most consequential frontiers in contemporary materials physics and engineering. This Perspective traces the evolution of thermal transport science from its empirical origins through the current AI-driven renaissance. We examine the limitations of conventional density-functional-theory-based phonon workflows, the emergence of universal machine learning interatomic potentials (uMLPs), graph-neural-network screening architectures such as the Crystal Attention Graph Neural Network (CATGNN), and generative inverse-design frameworks including the Physics-Guided Crystal Generative Model (PGCGM) and InvDesFlow-AL. Representative discovery and AI opportunities—including a computationally predicted room-temperature κ_L of 0.071 Wm⁻¹&#xa0;K⁻¹ in Cs₂HgPtCl₆ and approximately 1,100 Wm⁻¹&#xa0;K⁻¹ in metallic θ-TaN—are presented as concrete demonstrations of AI-driven computational power and human physical intuition, respectively. We conclude with a forward-looking discussion spanning five frontier challenges: machine learning frameworks for phonon–electron and phonon–ion interactions (with emphasis on electron–phonon coupling and its role in superconductivity, thermoelectrics, and carrier mobility); interpretable and symbolic AI approaches that extract closed-form physical principles from learned representations; out-of-distribution generalization strategies essential for discovering genuinely unprecedented materials; autonomous self-driving laboratory ecosystems that close the loop between computational prediction and experimental validation; and AI-accelerated design of interfacial thermal transport for high-power electronics and data center thermal management.</p>