The general cross section is expressed in terms of Stokes parameters of incoming and detected radiation. The dependence on the experimental arrangement is made explicit. Circular dichroism is considered for both randomly oriented and polarized target systems. A simple example illustrates how incident left- and right-handed circularly polarized x-rays can be used to obtain orientational information. We also examine the validity of the impulse (Compton) and optical (Raman) approximation for scattering by 1s electrons of hydrogen and hydrogen-like ions using an exact scaling law.