Recent research has demonstrated the potential role of topological defects in crucial cellular functions including morphogenesis, physiology and development, and programmed cell death. Yet, in the context of biophysical and biomedical applications, we still lack a mechanistic framework that takes into account the role of long-range order and topological defects in the emergent dynamics of mass, momentum, and energy transport. Owing to the coupling between surface, hydrodynamic and elastic fields, anisotropic fluids experience a range of topological constraints within micro-scale confinements, triggering the evolution and sustenance of flow-induced topological features which can be tuned as a function of tractable micro-environmental parameters like geometry, temperature and pH.Topological Fluid Mechanics will zoom into the dynamics of the generation and annihilation of topological structures in complex and biological fluids, and assess the emergent functionalities – both material and biological – of such structures within model and natural living matter systems. The line of research planned here will address current chasms through careful experiments, statistical analyses, and theoretical modelling, thereby accounting for the coupling between topology and cellular properties and performance. A key novelty of TOPOFLUME will be the investigation of spontaneous flows that emerge in such active systems. Although spontaneous flows have been reported in model cellular systems, their functional role in natural systems is yet to be ascertained. By revealing the mechanistic underpinnings, TOPOFLUME will bring about a paradigm shift in the domain of micro-scale transport phenomena, that will allow us to explore and employ such fluids as complex functional materials, thus significantly broadening the conventional microfluidic and biomaterial perspectives. Further afield, this unique approach will lay the mechanistic foundations to decode emergent micro-scale transport processes in cell biology and biomedical flows, leading to innovative approaches to diagnostic and bioremediation techniques.