Tetris is a popular puzzle video game, invented in 1984. We formulate two
versions of the game as a transformation semigroup and use this formulation to
view the game through the lens of Krohn-Rhodes theory. In a variation of the
game upon which it restarts if the player loses, we find permutation group
structures, including the symmetric group $S_5$ which contains a non-abelian
simple group as a subgroup. This implies, at least in a simple case, that
iterated Tetris is finitarily computationally universal