ZZ Variants
*Thanks to Joseph Tudor (PapaSmurf) for providing information on the modern ZZ variant classification and Dylan Nyein (Raven) for some ZZ-D information.
ZZ-A (α)
The modern classification of ZZ-A is that it is when the first two layers are solved without any intentional influencing of the last layer. So the steps would be EOCross or EOLine > F2L > ZBLL / OCLL+PLL / COLL+EPLL / Any last layer method. Zborowski's original description of ZZ-A focuses on ZBLL as the last layer method.
ZZ-B (β)
ZZ-B covers any partial last layer influencing during the first two layers. Phasing then ZZLL (Zborowski's original version of ZZ-B) and ZZ-R are examples of ZZ-B.
ZZ-C (γ)
ZZ-C includes sub-variants which completely orient all corners before getting to the last layer. Winter Variation and OLS are a couple of examples. The original version of ZZ-C as proposed by Mitchell Stern was to orient all last layer corners while solving the final F2L pair.
The original version of ZZ-C was proposed by Mitchell Stern.
ZZ-D (δ)
ZZ-D is any variant that permutes all corners before getting to the last layer. The original version of ZZ-D was to permute all corners while solving the final pair on the left side of the first two layers then complete the right side of the first two layers and end the solve with 2GLL. Zborowski's website included a couple of other corner permutation variants, E and F. The E variant permutes all corners while solving the final F2L pair. The ZZ-F variant, as proposed by Grzegorz Łuczyna, has the steps of EOLine > 1x2x2 on the left and 1x2x2 on the right > permute all corners while solving the last pair of the left side > last pair and last layer. The E and F variants have since been grouped under the ZZ-D variant to have a single variant focused on corner permutation with several sub-variants.
The original version of ZZ-D
https://web.archive.org/web/20090302093157/http://speedcubing.com.pl/nooks_zz.htm#zzspeed_warianty_d
Zbigniew Zborowski had the idea of early corner permutation on his website, but states that he hasn't yet found a way to do it.
Kim Orbit developed a recognition method and the algorithms in 2012.
https://www.speedsolving.com/threads/at-last-zz-d-method-has-been-completed.34994/#post-705181
This was for when the final pair is already built. The algorithms permute the corners while inserting the built pair.
In 2020, Dylan Nyein decided to develop the complete version for any last pair corner and edge situation.
Dylan Nyein and Joseph Tudor together completed the development.
Joseph Tudor proposed a new corner permutation variant in July, 2018.
Steps:
EOLine + permute DBL corner.
Permute all corners while ensuring that all pieces of the left block are in the U and L layers.
Complete left side 1x2x3 using U and L turns.
Right side 1x2x3.
2GLL.
ZZ-CT
Chris Tran's original idea was HW.
TTLL was taken from a method called Navi proposed by user elrog on the SpeedSolving.com forum in 2014.
CT was proposed in May 2016.
ZZ-EF
On December 30, 2014 SpeedSolving.com user MrMan proposed a ZZ variant that solves all edges and ends with two COLL algorithms.
That same day, Matt DiPalma refined MrMan's idea into a usable variant with no parity issues.
The next day, DiPalma made an official proposal in the form of a new topic on SpeedSolving.com.
ZZ-Portico
ZZ-Portico was proposed in May, 2012.
WaterZZ
The idea for WaterZZ was first mentioned by Joseph Tudor in June, 2018.
The steps were refined to their current form in November, 2018.
Tripod
In August 2017, Max Garza (Neuro) proposed and developed NLS
NLS solves the last slot in ZZ while preserving a 1x2x2 block on the last layer. Then the last layer is solved using a single algorithm.
In September 2023 Ryan Hudgens (OreKehStrah) proposed TLS
With TLS, the user intuitively solves a U layer corner and edge pair into the last slot. Then the TLS algorithm solves the corner and edge pair that belongs in that last slot while also matching up the U layer pair with its edge on the U layer to form a 1x2x2 block.