List of Scattering Phenomena While at lunch with my lab group we got into discussion of the different types of scattering phenomenon that we encounter in everyday life and physical experiments. We ended up listing about a dozen or so types of scattering that we see constantly, but I left unfulfilled.
I want to compile a list of scattering phenomenon and a brief description. At the very least this will be helpful for those taking the physics GRE in the near future, otherwise its a good exercise for anyone interested in physics, even those in professional physics.
I'll Begin to give you the basic jist of what I'm looking for, feel free to elaborate on the description as much as you want. An equation is useful if it's easily expressed
Compton scattering: Scattering of a photon off of a particle, photon imparts momentum to the particle and loses some of its energy, the change in wavelength is described by 
$$\Delta_{\lambda} = \frac{h}{mc}(1-\cos{\theta})$$
It is independent of the frequency of the incoming photon and inversely proportional to the mass of the particle scattered from. 
Raleigh Scattering: Elastic Scattering of photons off of molecules and other (micro and macro) particles, photons do not lose energy but change direction. Has a strong dependence on frequency and is the reason the sky is blue (and why you can see laser pointer beams in the dark). 
P.S. I don't have the reputation to create tags yet, and there are no tags relevant to this question (big-list scattering) please feel free to retag as necessary 
 A: Mie scattering: The exact Theory to which Raleigh Scattering is the small particle approximation.
A: Scattering, interpreted broadly is just "probe with wave or particle" and "measure response" and thus I claim that it is the principle behind most if not all experimental techniques in physics.  
Most of the scattering techniques I give below are "just" applications of Rayleigh scattering, but I hope you can see that the simplicity of Rayleigh scattering is precisely what makes them useful experimental tools!
X-ray and neutron scattering experiments are used to find the structure of complicated materials, for instance.  The keyword here is "Bragg's law" in the case of crystal lattices. 
A popular technique to probe dynamics is "Dynamic light scattering".  The principle here is that scattering can detect fluctuations due to Brownian motion in complex fluids, and this information is encoded in the autocorrelation of the measured intensity.  
With scattering experiments, you might think you're screwed if your probe scatters multiple times before it comes back to your detector (because then how will you be able to interpret the data).  However, Diffusing wave spectroscopy is a very clever technique that applies in the presence of multiple scattering events.
The field of acoustics is all about scattering of sound waves.  In materials there's a lot of interest in studying phonons - these are also probed via scattering of various types.
In the generalized interpretation of scattering, conductivity / resistivity measurements in hard condensed matter also become scattering experiments.  There you probe with a electromagnetic wave by causing the voltage in a wire to your sample to oscillate, and you measure the response in the form of electron current.  Examples of recently popular materials studied this way: high-temperature superconductors, integer and fractional quantum Hall devices, graphene, topological insulators, etc.
And obviously, from this point of view, particle colliders and detectors do a kind of scattering experiment as well.
The list goes on and on.  Many, if not most things studied in physics are waves of some sort, and thus scattering processes are very relevant to experiments.  One prominent non-example is most of astrophysics, where we have no chance of actually probing the stars ourselves and can only observe what they do on their own.  You might argue that astrophysics is therefore just "observational" and not "experimental".
A: The inverse process of Compton scattering (Inverse Compton) is a process where a relativistic charged particle scatters a low energy photon and boosts its energy by an amount proportional to the square of the Lorentz factor of the particle
$$\epsilon_1=4\gamma^2\epsilon_0$$
This process is very important in Astrophysics. It is one of the basic mechanism that produce gamma radiation in AGNs.
An other process that could be considered as a scattering process is the gravitational deflection of light from the Sun or any other massive object. That process can be described as if the space-time is a medium of variable refractive index
$$n=\sqrt{1+\frac{2a^2GM}{c^2r^3}}$$
where alpha is the minimum distance of the light beam from the Sun.
Finally, in quantum mechanics, one can consider the scattering of particles by a potential. The description is given with the help of the wavefunction, where the particles are described as waves which are transmitted across, or reflected by the potential.
