An overview on the recent developments in the field of liquid crystalline bent-core molecules (so-called banana liquid crystals) is given. After some basic issues, dealing with general aspects of the systematisation of the mesophases, development of polar order and chirality in this class of LC systems and explaining some general structure–property relationships, we focus on fascinating new developments in this field, such as modulated, undulated and columnar phases, so-called B7 phases, phase biaxiality, ferroelectric and antiferroelectric polar order in smectic and columnar phases, amplification and switching of chirality and the spontaneous formation of superstructural and supramolecular chirality.

This critical review focuses on recent progress in the field of T-shaped ternary amphiphiles. These molecules can self-assemble into a series of new liquid crystalline (LC) phases with polygonal cylinder structures, new lamellar phases and LC phases combining columns and layers. These structures are analyzed on the basis of symmetry, net topology and tiling pattern (Laves and Archimedean tilings) and discussed in relation to morphologies of multiblock copolymers, self organized DNA super-lattices, metal–organic frameworks, crystal-engineering and self-assembled periodic superstructures on surfaces (210 references).

An overview over the current state of research in the field of biaxial nematic liquid crystalline materials is given. After a short introduction, providing some general aspects and summarizing the classical approaches, the main part focuses on recent developments of new concepts for designing biaxial nematics. First, the major theoretical concepts are outlined, including the classification to different symmetries, the importance of cooperativity and cluster formation for the development of biaxial order and the conditions for the establishment of field induced and spontaneous biaxiality in nematic phases. These new concepts also require the re-evaluation of the tools used for the identification of phase biaxiality, which are discussed briefly. In the second part, recent progress in the design of potential biaxial nematic materials, especially focussing on bent-core molecules with nematic phases, is reported and, finally, comparisons with phase biaxiality as observed in smectic liquid crystals are made.

Bent-core mesogens derived from 4-cyanoresorcinol with terminal alkyl chains have been synthesized and investigated by polarizing microscopy, XRD and electro-optical methods. Short chain compounds have exclusively nematic phases which can be cooled to ambient temperature. These nematic phases are similar to ordinary nematic phases with only nearest neighbour correlation (N) whereas long chain compounds form SmC-type cybotactic clusters and these cybotactic nematic phases (N_cybC) can be regarded as strongly fragmented SmC phases. The chain length dependent as well as temperature dependent structural transition from N to N_cybC is continuous and associated with a change of the position and intensity of the small angle scattering in the XRD patterns. Moreover, a temperature dependent stepwise transition from cybotactic nematic phases to different types of non-polar and tilted smectic phases (SmC _(I) and SmC _(II)) is observed with a mesophase composed of elongated, but not yet fused cybotactic clusters (CybC) as an intermediate state of this transition. This improves the understanding of the nature and special properties of the nematic phases formed by bent-core molecules as well as their transition to smectic phases and it paves the way to new materials with spontaneous or field-induced biaxial nematic phases at ambient temperatures.