Consider a set of n pairwise disjoint axis-parallel rectangles in the plane. We call this set the source rectangles S. The aim is to move S to a set of (pairwise disjoint) target rectangles T . A move consists in a horizontal or vertical translation of one rectangle, such that it does not collide with any other rectangle during the move. We study how many moves are needed to transform S into T . We obtain bounds on the number of needed moves for labeled and for unlabeled rectangles, and for rectangles of different and of equal dimensions.