  We review progress in active hydrodynamic descriptions of flowing media on
curved and deformable manifolds: the state-of-the-art in continuum descriptions
of single-layers of epithelial and/or other tissues during development. First,
after a brief overview of activity, flows and hydrodynamic descriptions, we
highlight the generic challenge of identifying the dependence on dynamical
variables of so-called active kinetic coefficients -- active counterparts to
dissipative Onsager coefficients. We go on to describe some of the subtleties
concerning how curvature and active flows interact, and the issues that arise
when surfaces are deformable. We finish with a broad discussion around the
utility of such theories in developmental biology. This includes limitations to
analytical techniques, challenges associated with numerical integration,
fitting-to-data and inference, and potential tools for the future, such as
discrete differential geometry.
