What are some of the most interesting Feynman diagrams?

One of the most famous ones I have come across is called the Penguin diagram. They represent quark interactions via a W or Z loop. According to Wikipedia, they are important for understanding CP violation in the standard model (I don't know much about the technical details). read more

In quantum field theory, a tadpole is a one-loop Feynman diagram with one external leg, giving a contribution to a one-point correlation function (i.e., the field's vacuum expectation value). read more

The Feynman diagram representation of a process is most useful when a few relatively simple diagrams supply most of the answer. That is the regime physicists call “weak coupling,” where each additional complicating line is relatively rare. read more

Most Feynman diagrams are much more complicated than this simple example. An electron interacting with the field of a magnet, for example, can emit a photon and then re-absorb the same photon, called a ‘virtual’ photon, after it has interacted with a photon from the magnet. read more