This article discusses some objects made of ivory, consisting of nested spheres which can rotate freely inside each other. These objects are known as the “Chinese puzzle balls” and became quite popular in Europe during the 19th century. The methods used by the artists to create them in the carved ivory can be considered as the real "puzzle" of the balls. Actually, Europe had its production of puzzle balls too. During the 16th and 17th centuries, “contrefait balls”, or “contrefait Kugeln”, were carved in ivory with the geometry of a sphere or of a Platonic solid, frequently of a dodecahedron. They were items for the Cabinets of Curiosities, the rooms of wonder that had their roots in the culture of the Renaissance Courts. Today, these European ivory items, which are exceedingly rare, are exhibited by museums and collections. Here we discuss both the Chinese and European objects.