In this talk, we consider an isoperimetric problem for planar Tilings allowing for unequal repeating cells. We discuss general existence and regularity results and we study the classification of planar isoperimetric double Tilings, i.e. with two repeating cells. In this case, we explicitly compute the associated energy profile and we give a complete description of the phase transitions. Based on joint works with M. Novaga and E. Paolini.