Various materials have been found to "catalyze" carbon nanotube growth in chemical vapor deposition (CVD) when they become nano-sized particles. These involve not only metals, such as Pd, Pt, Au, Ag, and Cu, but also semiconductors, such as Si, Ge, and SiC. Alumina and diamond nanoparticles also produce carbon nanotubes. These "catalysts", which are better called "seeds", can be categorized into two types: one type forms a eutectic liquid or highly-mobile alloy with carbon, and carbon atoms precipitate from the eutectic alloy; the other type remains as a solid phase and form a carbon surface layer during CVD growth. In this paper, we review recent studies of SWCNT growth with these non-iron-group materials and highlight the mechanisms involved.