First introduced by Pointcheval and Stern, the forking lemma is commonly used in proofs of security to demonstrate a reduction to breaking some known-to-be-hard mathematical problem. While the original forking lemma is straightforward, keeping up with the number of variations of forking lemmas in the literature (and why each variant exists) is... not.

I wrote a short (informal) note that reviews the original forking lemma and several variations thereof, and discusses the differences among each variant. You can find the note here.