theres two types - elastic and inelastic. Elastic scattering involves no (or a minute) loss or gain of energy by the radiation, inelastic scattering does involve some change in the radiations energy. closly linked to the kinetic theory of the collision of solid bodies.
there are alot of different scattering experiments -
Brillouin scattering: occurs using photons, measures magnetic spin i think.
Compton scattering: uses X-ray or gamma ray photons, i think its used to measure atomic nucli
Rayleigh scattering: uses particles smaller than the wavelength of light, its the theory of why the sky is blue.
Thomson scattering: uses a charged particle to scatter of electromagnetic radiation.
there are more theories but im very rusty on all of this so you might want to check them over.