Some of the chains on this page are more of a "proof of concept", rather than a real form.
A reversible chain has two trigger points, each at a different end of the chain.
Kamaitachi (かまいたち) is a special type of base that doubles as a Hellfire and can potentially be reversible.
A derivative of Kamaitachi invented by Kame, Kameitachi (かめいたち) functions in the same way. For reference, watch this video.
(昇竜連鎖) A chain that climbs upwards. This makes sandwich an incredibly useful form to know.
Two-on-Two Stacking (ニコニコ積み) refers to this style of chaining:
A Same-Color Chain (同色連鎖) has two separate, same-colored groups pop consecutively.
Kenny Formula refers to the most popular 19 Chain.
A group of Puyo in the hidden 13th row won't pop unless it drops down to Row 12 or lower. A Ghost Chain (幽霊連鎖) takes advantage of this mechanic.