How do hexatics flow? Forty years after Nelson’s and Halperin’s first prediction of the existence of this phase of two-dimensional matter, intermediate between crystalline solid and isotropic liquid, this seemingly elementary question is still unanswered. Whereas the delicate nature of hexatics could partially justify this oversight, recent findings in tissue mechanics have created the urgent demand to fill this gap, by providing this phase with unexpected biological relevance. Like two-dimensional crystals on the verge of melting, tissues are often neither ordered solids nor disordered liquids, but inhabit a continuum of intermediate states known as the epithelial-mesenchymal spectrum. This versatility lies at the heart of a myriad of processes that are instrumental for life, such as embryonic morphogenesis and wound healing, but also of life-threatening conditions, such as metastatic cancer. Understanding the physical origin of these mechanisms requires going beyond the current hydrodynamic theories of complex fluids and introducing a new theoretical paradigm, able to account for hexatic order and biomechanical activity. This multidisciplinary program aims to develop a systematic theory of hexatic hydrodynamics and use it to gain insight into the physical mechanisms underpinning the dynamics of tissues and the progression of metastatic cancer. The program will consist of three themes. First we will develop the necessary formalism to describe viscous flow in hexatics. Next, we will extend it to tissues and investigate the interplay between hexatic order, activity, topological defects and flow. Finally, we will use the new framework to explore the first three steps of the metastatic cascade: 1) the detachment of clusters of mesenchymal cells from the primary tumour; 2) their subsequent invasion of the extracellular matrix; and 3) their translocation across blood vessels, which allows metastases to enter into the bloodstream and disseminate to distant organs.