The non-equilibrium dynamic behaviors of soft materials such as cells and tissues are complex due to the nature of activity. These dynamic behaviors are widely observed in various physiological and pathological processes such as embryonic development, tissue regeneration and cancer metastasis. In recent years, researchers have continuously revealed the potential physical mechanisms and functions behind these complex dynamic behaviors in order to deepen the understanding of living systems. This review focuses on the research status of the dynamics of active liquid crystals and introduces the research progress in recent years. First of all, we introduce some representative theoretical models describing active soft matter, such as discrete models, particle models, cell vertex models, etc., and continuous models, such as active liquid crystal theory, active gels theory, etc. We focus on the theory of active liquid crystal. Considering the polar properties of cells, bacteria and protein fibers, active liquid crystals can be specifically divided into polar active liquid crystals and non-polar nematic active liquid crystals. The interaction between the former units is obvious head alignment and tail alignment, and then the latter only considers the interaction of local alignment, and does not distinguish between the head alignment or tail alignment of the units. The active gels model is a theoretical model that mainly considers the viscous dissipation of microscopic particles and fluid media, rather than substrate friction. Such systems can be regarded as a gel with typical visco-elastic properties, such as cytoskeleton extracts. In addition, we introduce the relevant research on topological defect dynamics. In the active liquid crystal system, the distortion of the local orientation field often occurs, forming topological defects, such as +/- 1/2 defects and +/- 1 defects. In the nematic systems, by solving the Stokes equation, researchers found that the activity would drive the directional propulsion of the +1/2 defect, while the-1/2 defect stops in place; Other studies analyzed and solved the spiral +1 topological defect in the polar system. In recent years, many experiments have shown that topological defects have important physiological significance for regulating cell function and homeostasis in tissues. In addition, researchers also tried to regulate the dynamic behavior of +/- 1/2 topological defects by controlling boundary constraints, chirality, outfield and substrate properties. Finally, from the perspective of biological interface, the theoretical model of the active nematic liquid crystal interface is introduced. The phase field method is often used to describe the interface problem of active liquid crystals. Here, the specific form of the governing equation of biological interfaces, the spatial discrete form of different field variables and the corresponding integral calculation method are described. Relevant studies have shown that activity, stiffness and other factors can regulate the interface morphology. In addition, the motion characteristics of the topological defects are closely related to the evolution of the interface. The specific performance is that the +1/2 defect driven by contractile activity will turn away from the interface, which is conducive to the stability of the interface, while the +1/2 defect driven by the extensile activity crosses the interface, thus disrupting the interface.
