At the cake meeting [weekly condensed matter theory group meeting] we took three weeks to go through the review article Inelastic light scattering from correlated electrons by Devereaux and Hackl.
I found it very helpful. Here are a few things I learnt.
It is sensitive to anisotropy in Fermi surface properties via different light polarisations. This is because the relevant matrix elements depend on the polarisation.
In principle this can be used to detect unconventional superconductivity and even distinguish d-xy and d_x2-y2.
This polarisation dependence also shows signs of anisotropies in the metallic state of cuprates.
Background electronic continuum
In a simple metal the scattering off electron-hole pairs should cutoff at a wavevector of about v_F q where v_F is the Fermi velocity and q is the change in wavevector of the light. This is a relatively small energy. However, in strongly correlated materials such as the cuprates this extends to much higher energies. This is still not really understood.
Electronic Raman scattering played a key role in the cuprates in two regards. First, via two magnon scattering it provided the first experimental estimate of the antiferromagnetic exchange interaction J in the parent Mott insulator. [n.b. most people would agree that the large J is at the heart of the high-Tc]. Second, it showed the large "incoherent" background which is linear in omega, having a large influence on the development of the Marginal Fermi liquid phenomenology.
I was a little disappointed to see that interpreting the experimental results is not completely straightforward and that often there was a fair bit of noise in the data.
Overall it seems this is a promising technique which provides a complementary probe to others such as ARPES, optics, and transport measurements. No doubt in the next few decades there will be technological advances that will increase resolution and increase the signal to noise. It would be nice to see some measurements on organic superconductors.