At thermal equilibrium, chiral molecules form a range of liquid-crystalline phases, such as the cholesteric which presents a helical structure of the molecular orientation. Chirality, though essential to the construction of the cholesteric, is totally absent in its long-wavelength hydrodynamics, which is identical to that of the achiral smectic-A liquid crystal. This cloaking of chirality, however, relies on the existence of an energy function for the dynamics. I will talk about how macroscopic mechanics of active layered phases carry striking chiral signatures. Thanks to the mix of solid and liquid-like directions, the chiral active stresses create a force density tangent to contours of constant mean curvature of the layers. This non-dissipative force in a fluid direction – odder than odd elasticity – leads, in the presence of an active instability, to spontaneous vortical flows arranged in a two-dimensional array with vorticity aligned along the pitch axis and alternating in sign in the plane.

In addition, I will discuss how odd elasticity, an effect that is attracting much current attention, is naturally realised in polar and chiral columnar systems. The resulting oscillatory mode, thanks to the Stokesian hydrodynamic interaction, has a nonzero frequency on macroscopic scales, set by the ratio of the coefficient of chiral and polar active stress and the viscosity. A bulk columnar phase undergoes a spontaneous buckling instability due to extensile activity. If the active units composing the columnar state are, in addition, chiral, the twisted columns host large-scale shear flows due to a new form of odd elasticity.