The 7x7x7 cube (normally referred to as the 7x7x7 or 7x7) is a twistable puzzle in the shape of a cube that is cut six times along each of three axes. The main brand for this puzzle is the V-Cube, which was patented by Panagiotis Verdes. Many other cube companies have produced puzzles very simular, but these are considered knock-offs. It is the smallest cube to be rounded (or 'pillowed') because it is mathematically impossible to make a perfectly cubical 7x7x7 cube without any kind of magnets or locking mechanism, as the corners would fall off.
Shengshou have made a cubic 7x7, and it has become very popular; specifically the smaller version.
This puzzle has 6 fixed centers, a total of 144 other center pieces, a total of 60 edge pieces, and 8 corners, and has 2.0 * 10^160 positions. It is probably thus the most complex twisty puzzle on the market today.