  We present an experimental study of the quasi-elastic Raman scattering (QES)
of plane-wave and twisted light by liquid crystals. Depending on their
temperature, these crystals can exhibit isotropic, nematic and chiral nematic
phases. The question is addressed of how the phase of a crystal and the state
of incident light can affect the quasi-elastic energy spectra of the scattered
radiation, whose shape is usually described by the combination of Lorentzian
and Gaussian components. Special attention is paid to the \textit{chiral
phase}, for which the Raman QES spectrum is dominated by a Lorentzian with
reduced linewidth, pointing to diminished disorder and configurational entropy.
Moreover, this phase is also known for a regime of iridescence (selective
backscattering) which arises when the wavelength of incident light becomes
comparable with the chiral pitch length. Detailed measurements, performed in
this \textit{resonant} regime and by employing twisted light, carrying various
projections of the orbital angular momentum (OAM), have indicated a low-energy
scattering surplus depending on OAM. We argue that this observation might
indicate a transfer of angular momentum between light and the liquid crystal.
