Using direct-imaging cryogenic transmission and scanning electron microscopy, we show different stages of liquid-crystalline phase development in progressively more concentrated solutions of carbon nanotubes in chlorosulfonic acid: a dilute phase of individually dissolved carbon nanotubes; semidilute and concentrated isotropic phases; coexisting concentrated isotropic and nematic phases in local equilibrium with each other; and a fully liquid-crystalline phase. Nanometric resolution of cryogenic electron microscopy reveals carbon nanotube self-assembly into liquid-crystalline domains of several nanometers in width at very early stages. We find significant differences in carbon nanotube liquid-crystalline domain morphology as a function of the carbon nanotube aspect ratio, diameter, and degree of purity.