Liquid Crystals are a state of matter that have properties between those of conventional liquid and those of a solid crystal. Thermotropic liquid crystals react to changes in temperature or, in some cases, pressure. The reaction of lyotropic liquid crystals, which are used in the manufacture of soaps and detergents, depends on the type of solvent they are mixed with. Since the accidental discovery of the chiral nematic (ordered) phase in 1888 many liquid crystal phases have been found, sometimes by chance and sometimes by design. The existence of one such phase was predicted by Freiser in 1970, this was the biaxial nematic phase which has biaxial symmetry in contrast to that of the ubiquitous nematic phase which ix uniaxial. The biaxial symmetry of the predicted phase confers on it an additional layer of fascinating complexity. This book is devoted to the biaxial nematic phase, both lyotropic and thermotropic, formed by low molar mass as well as polymeric systems. It brings together theory, simulations and experimental studies. The book opens with a general introduction to the biaxial nematic phase, while chapters 2-7 discuss current theories and predictions. Chapters 8 and 9 report on alignment and applications, while chapters 10.1 -10.5 detail characterization with the goal of unambiguous identification. Final chapters (11-14) cover Lyotropic, Colloidal, Thermotropic and Low Molar Mass Thermotropic Systems respectively.