We review the research on carbon nanotube (CNT) dispersion in liquid crystals (LCs), focusing mainly on the approaches where the aim is to align CNTs along the LC director field, but also covering briefly the proposed possibility to enhance thermotropic LCs by CNT doping. All relevant LC types are considered: thermotropic LC hosts allowing dynamic CNT realignment, lyotropic LC hosts allowing very high concentration of CNTs uniformly aligned over macroscopic areas and consequent removal of the LC, and LC phases formed by CNTs themselves, used in spinning high-quality carbon nanotube fibres. We also discuss the issue of CNT dispersion in some detail, since successful nanotube separation is imperative for success in this field regardless of the type of LC that is considered. We end by defining a few major challenges for the development of the field over the next few years, critical for reaching the stage where industrially viable protocols for LC-based CNT alignment can be defined.