Active topology and morphology emerging in living systems

The intricate relationship between topology and morphology in living systems arises from their fundamental non-equilibrium nature. From the cytoskeleton to tissues, sustained energy input gives rise to robust topological structures, such as defects, and drives large-scale morphological transformations. In this review, we examine the topological principles governing collective dynamics and the role of topological defects as organizing centers in complex processes such as three-dimensional morphogenesis. Furthermore, we discuss the potential of defect manipulation via boundaries, external fields, or activity patterning, combined with control-theoretic and interfacial-regulation strategies, to enable the design of active materials and the control of morphological self-assembly. Finally, we outline future challenges in multiscale modeling, experimental characterization, engineering applications, and elucidating the physiological implications of topological morphogenesis.