Single-walled carbon nanotubes (SWNTs) have shown great potential in various applications attributed to their unique structure-dependent properties. Therefore, the controlled preparation of chemically and structurally pristine SWNTs is a crucial issue for their advanced applications (e.g., nanoelectronics) and has been a great challenge for two decades. Epitaxial growth from well-defined seeds has been shown to be a promising strategy to control the structure of SWNTs. Segments of carbon nanotubes, including short pipes from cutting of preformed nanotubes and caps from opening of fullerenes or cyclodehydrogenation of polycyclic hydrocarbon precursors, have been used as the seeds to grow SWNTs. Single-chirality SWNTs were obtained with both presorted chirality-pure SWNT segments and end caps obtained from polycyclic hydrocarbon molecules with designed structure. The main challenges of nanocarbon-segment-seeded processes are the stability of the seeds, yield, and efficiency. Catalyst-mediated SWNT growth is believed to be more efficient. The composition and morphology of the catalyst nanoparticles have been widely reported to affect the chirality distribution of SWNTs. However, chirality-specific SWNT growth is hard to achieve by alternating catalysts. The specificity of enzyme-catalyzed reactions brings us an awareness of the essentiality of a unique catalyst structure for the chirality-selective growth of SWNTs. Only catalysts with the desired atomic arrangements in their crystal planes can act as structural templates for chirality-specific growth of SWNTs. We have developed a new family of catalysts, tungsten-based intermetallic compounds, which have high melting points and very special crystal structures, to facilitate the growth of SWNTs with designed chirality. By the use of W6Co7 catalysts, (12,6) SWNTs were directly grown with purity higher than 92%. Both high-resolution transmission electron microscopy measurements and density functional theory simulations show that the selective growth of (12,6) tubes is due to a good structural match between the carbon atom arrangement around the nanotube circumference and the metal atom arrangement of (0 0 12) planes in the catalyst. Similarly, (16,0) SWNTs exhibit a good structural match to the (116) planes of the W6Co7 catalyst. By optimization of the chemical vapor deposition (CVD) conditions, zigzag (16,0) SWNTs, which are generally known as a kinetically unfavorable species in CVD growth, were obtained with a purity of ∼80%. Generally speaking, the chirality-specific growth of SWNTs is realized by the cooperation of two factors: the structural match between SWNTs and the catalysts makes the growth of SWNTs with specific chirality thermodynamically favorable, and further manipulation of the CVD conditions results in optimized growth kinetics for SWNTs with this designed chirality. We expect that this advanced epitaxial growth strategy will pave the way for the ultimate goal of chirality-specified growth of SWNTs and will also be applicable in the controlled preparation of other nanomaterials.