The liquid-crystalline state of matter (mesomorphic state, or mesophase) is intermediate between the crystalline and liquid states, simultaneously showing some of the anisotropic properties of solids and the fluidity of liquids [10]. In this state, materials demonstrate a tendency to flow like liquids and have some properties similar to solids. LCs may be divided into two main classes, named thermotropics and lyotropics [2,6,11]. Amphotropic LCs that show both thermotropic and lyotropic phases were also identified [12,13]. For example, exhibition of amphotropic LC properties has been reported for many amino acid, peptide, phospho- and glycolipid-based LCs, with a special attention to the LC-like structure of cell membranes [14,15,16]. The properties of polymeric and elastomeric LC phases were also discussed [17,18,19,20]. These materials combine polymer network properties with LC anisotropy, and they are good candidates for stimuli-responsive reversible shape memory materials [21]. The different polymer-modified LCs (e.g., a continuous polymer matrix with the inclusion of LC droplets or a bicontinuous system of a polymer network dispersed in an LC host) also represent a great interest for different practical applications [22].

For the completeness, it can also refer to important classes of unconventional LCs. The two main categories related to supermolecular and supramolecular systems were highlighted (for a recent review, see [23]). The different types of ionic LC versatile materials (dendrimeric thermotropic, polymeric, lyotropic, zwitterionic, and mesoionic) were also identified [24,25].

Thermotropic LCs demonstrate the presence of LC phases in a certain temperature range between the crystalline solid and isotropic liquid. Therefore, in these materials, the mesomorphic state formation depends on temperature. These substances with anisotropically shaped molecules demonstrate the dual characteristics of solids and liquids. They have some sort of positional or orientational order and may flow like a liquid. This duality can lead to anisotropy in optical, viscoelastic, electrical, and magnetic properties. On the basis of molecular shape, the LCs can be classified as calamitic (rod-like molecules), discotic (disc-like molecules), and bent-core (banana-shaped molecules with bent cores and flexible tails) types; other more exotic types (e.g., bowlic) have also been reported. Nowadays, huge quantities of thermotropic LC substances (more than 70,000) with different chemical compositions and phase transition temperatures have been discovered [26,27].

The main thermotropic LC phases are nematics, smectics, and cholesterics [28,29,30]. In the simplest nematic LCs, the molecules are preferentially oriented along a single director axis, but they have no positional order. In the smectic LCs phases with positional layered order, the molecules have a long-range orientational order and are organized positionally in smectic layers. In smectic A and smectic C phases, the molecules are oriented along the layer normally and at an oblique angle to the normal angle, respectively. There also exist many other types of smectic arrangements (B, D, E, F, etc.) with more complex self-organization. In the cholesteric (chiral nematic) LC phase, the director shows a helical structure and the molecules are arranged along a director axis with continuous changes of their directions in the form of a helix [28]. The helical period is typically in the range from 0.1 to 100 microns, with characteristics optimal for applications observed in more narrow ranges (10–20 μm in most cases). The more complex LC phases such as chiral nematic, chiral smectic, blue phases, and twist grain boundary phases were also identified [13], as well as most novel twist-bend and ferroelectric nematics [31,32]. The phase transitions between various LC phases can be first order, second order, or weakly first order. Nematic liquid crystals are the base of most modern displays, with OLEDs, despite recent spectacular developments, still lagging behind.

In lyotropic LCs, the phase transitions are induced by changes in the temperature and concentration of dissolved amphiphilic molecules (including the hydrophobic and hydrophilic blocks) in suitable solvents. In an aqueous environment, such molecules can be self-organized in different phases depending on their molecular structure [33,34]. At temperatures above Krafft point, boundaries called CMC curves between the unimer and aggregate solution (micellar, vesicle, or microemulsions) phases appear. Typically, lyotropic LCs demonstrate the different types of long-range periodicity, with amphiphilic molecules arranged in the nematic, hexagonal, lamellar, and different intermediate (e.g., cubic) phases [35]. In a lamellar phase, bilayers with hydrophilic head groups oriented to water are formed. In a hexagonal phase, the amphiphilic molecules are arranged as infinite cylindrical structures on a hexagonal lattice. A cubic phase may exist between the lamellar and hexagonal LC phases; in this phase, the arrangement is in the form of a lipid sphere in a dense cubic lattice. These LCs can be used as efficient systems in drug delivery [36]. Water-based lyotropic LCs are common in biological and living systems [37]. The phase diagrams for many surfactant/water systems can be found in the review [34]. The anisotropic colloidal particles (rod-like, plate-like, or their hybrids) can also form lyotropic LC phases. These structures are called nanomesogen lyotropic LCs [38].