The invention provides a modular storage system (1), comprising a plurality of box-shaped structural units(2,3,4,5,6,7,8,9,10,11,12,13,14), one or more of which are storage units used for storage, and each structural unit having front and back faces and left, right, top and bottom sides, wherein: the box-shaped structural units (2,3,4,5,6,7,8,9,10,11,12,13,14) are laterally attachable to each other side-by-side through attachment points (30,31,32,33,74,79,97,99) on the left and right sides, thereby to construct a joined structure of at least two of the structural units; and one or more of the box-shaped structural units are reversible structural units, in which the corresponding attachment points are positioned and shaped so that the reversible structural unit is attachable in the lateral side-by-side attachment so that the corresponding front faces of adjacent joined structural units are oriented either in one direction or in opposite directions.