Team Blindfolded (Team BLD) is a popular social activity for speedcubers. In Team Blindfolded, one cuber is blindfolded for the entire solve (including inspection) and communicates (mostly by listening) with another cuber about how to solve the cube. This is commonly accomplished by calling out a sequence of moves, or even special codes.
While it is not an official WCA event, Team Blindfolded has been held as an unofficial event at many competitions, and there have been some efforts to introduce it.
Ian Winokur and Bob Burton are known for being early proponents of Team Blindfolded since late 2005. They are responsible for the earliest calling system for Team BLD.
Since then, the event has spread all over the world, and a lot of cubers have come up with interesting variations: For a mystery puzzle at Worlds 2009, blindfolded cubers were paired with Japanese callers who didn't speak English. In November 2010, Tim Habermaas and Stefan Pochmann tried what might be called a Blindfolded Teamsolve. Their video can be found here.
Cubers have devised several calling systems to make it easier to tell each other moves without saying each one separately. Most of these are for the Fridrich Method. Cubers often come up with simple names for "trigger," "pull," push," "spin"/"rotate," but there have been attempts to make this more powerful and consistent.
Each F2L arrangement is given a name (most often a letter and a number), as well as each OLL and PLL. Cube rotations are communicated by "Spin Left/Right/Twice" for y, y', and y2, respectively ("right" and "left" correspond to where the F face is moved with the rotation).
HIJK (F2L Slots)
This system seems to have originated at Berkeley around 2009. Each F2L slot is given a letter, and a corresponding "pull" trigger:
|F2L||L' U' L|
|F2L||L U L'|
|F2L||R' U' R|
|F2L||R U R'|
These can be modified like letters for normal moves. For example, K2 = (RUR')(RUR') = R U2 R' , and K' = RU'R'. Cube rotations can be done using the "spin" terms, and LL algs can be called using any system.