  Living systems are chiral on multiple scales, from constituent biopolymers to
large scale morphology, and their active mechanics is both driven by chiral
components and serves to generate chiral morphologies. We describe the
mechanics of active fluid membranes in coordinate-free form, with focus on
chiral contributions to the stress. These generate geometric `odd elastic'
forces in response to mean curvature gradients but directed perpendicularly. As
a result, they induce tangential membrane flows that circulate around maxima
and minima of membrane curvature. When the normal viscous force amplifies
perturbations the membrane shape can become linearly unstable giving rise to
shape instabilities controlled by an active Scriven-Love number. We describe
examples for spheroids, membranes tubes and helicoids, discussing the relevance
and predictions such examples make for a variety of biological systems from the
sub-cellular to tissue level.
