<p>Carbon nanotubes (CNTs), as innovative materials, are driving technological advancements in multiple fields. However, the high-quality synthesis of CNTs is still constrained by the core issue of catalyst design. Although rich experience has been accumulated in the regulation of growth parameters (temperature/carbon source/atmosphere), precise control of the catalyst for the directional synthesis of target-structured CNTs still faces multiple challenges. In recent years, breakthroughs have been made in areas such as the innovation of catalyst synthesis methods (e.g., atomic layer deposition and dual-metal synergistic design), the analysis of catalytic active sites (metal–support interface effects), and the dynamic evolution mechanism (inhibition of Oswald ripening), laying the foundation for the development of customized catalysts. This article systematically reviews the research progress of CNTs growth catalysts: Firstly, it analyzes mainstream synthesis techniques such as sol–gel method and chemical vapor deposition, as well as their thermodynamic models; Secondly, it interprets the structure dynamic evolution (nucleation/coarsening/phase transformation) of the catalyst under high-temperature conditions and its structure–activity relationship with CNTs growth; Then, it categorically reviews the functional characteristics of iron/cobalt/nickel-based single and dual-metal catalytic systems; Finally, it looks forward to future development directions from dimensions such as anti-sintering design, chirality control, and in situ characterization. This review provides a theoretical framework and technical path for the directional design of high-performance catalysts.</p>