newtonandapple it's IKEA Besta units with Samla boxes. The units and boxes come in all different sizes and you buy the frames and then just as many shelves to go inside as you need because you can put them all in at any height.
Toddler crafts/activity organization. Ikea Besta. Double shelf unit. Bladis baskets. Gles green boxes. Glis little boxes. Samla large and small boxes. Drona bins. Pingla boxes. http://www.ikea.com/us/en/catalog/products/70134044/