The structure and properties of liquid crystalline suspensions filled by carbon nanotubes (CNTs) are critically reviewed. Special attention is paid to interactions between CNTs and molecules of the liquid crystals (LC), which lead to formation of ordered supramolecular structures. These structures, in turn, determine unique physical properties of LC + CNT suspensions, including electrical conductivity, dielectric permittivity, phase transitions, optical transmission, memory effects that can be used in electrooptic and optoelectronic devices, etc. Great variety of LC phases are considered as a host media, such as nematics, cholesterics, smectics of different types (including ferroelectrics), lyotropic, chromonic, ionic and hydrogen-bonded liquid crystals. Alongside multi-and single-walled carbon nanotubes, the suspensions can also contain the platelets of organoclays used for facilitation of CNT dispersing. Recent practical applications of LC + CNT suspensions and nanomaterials based thereon are also outlined.