A polyomino is called a rep-cube if it can be folded into a cube and can be partitioned into two or more polyominoes such that each of them can be folded into a cube. This new notion was proposed in 2016 based on two famous ideas of polyomino and rep-tile. Since then, the author and colleagues have investigated several properties of this notion from the viewpoint of the folding problem. In this survey, we give known results in the previous work with some new ones.