We give an expository account of our computational proof that every position of the Rubik's Cube can be solved in 20 moves or fewer, where a move is defined as any twist of any face. The roughly positions are partitioned into about two billion cosets of a specially chosen subgroup, and the count of cosets required to be treated is reduced by considering symmetry. The reduced space is searched with a program capable of solving one billion positions per second, using about one billion seconds of CPU time donated by Google. As a byproduct of determining that the diameter is 20, we also find the exact count of cube positions at distance 15.