Abstract Since the discovery of single‐walled carbon nanotubes (SWCNTs), great efforts have been dedicated to understanding their growth mechanisms, aiming to improve structural controllability during catalytic synthesis. However, owing to the final success of the controllable synthesis of SWCNTs, the large‐scale synthesis of SWCNTs of each type with high purity (such as 99.9999%) is still very far from the current state‐of‐the‐art technologies of SWCNT synthesis and is the holy grail target of the entire carbon society. Here, a comprehensive review of the controllable synthesis of SWCNTs is presented from the perspective of theoreticians. The integration of experimental successes and the underlying theoretical understanding, such as the theoretical understanding of experimental observations and experimental verification of theoretical predictions, are thoroughly discussed in this review. Herein, first, the development of a three‐stage model of SWCNT catalytic growth: cap nucleation, tube elongation, and growth termination is systematically reviewed. The review subsequently focuses on the progress of the controllable synthesis of SWCNTs on the basis of the catalyst design, environmental conditions, and seeded growth. Finally, the key successes in understanding SWCNT growth mechanisms and controllable synthesis are summarized, and the main challenges and potential routes for structurally controllable SWCNT synthesis are also discussed.