What are advantages and drawbacks of using different orders of Møller-Plesset perturbation theory?

I am about to do some research in computational chemistry, however, I do not understand one method: What is the difference between second order and third order, etc, Møller-Plesset perturbation theory? I understand that MP theories include electron correlation in comparison to Hartree-Fock and how CCSD(T) can model the dispersion forces between atoms even better, but I cannot get a grasp on the difference between MP2, MP3, MP4 etc.


Also, why would I choose to use MP3 over MP2? Especially when they can be divergent, so surely I could end up with huge discrepancies in my results?


