The possibility to attain ferromagnetic properties in transparent semiconductor oxides such as ZnO is very promising for future spintronic applications. We demonstrate in this review that ferromagnetism is not an intrinsic property of the ZnO crystalline lattice but is that of ZnO/ZnO grain boundaries. If a ZnO polycrystal contains enough grain boundaries, it can transform into the ferromagnetic state even without doping with “magnetic atoms” such as Mn, Co, Fe or Ni. However, such doping facilitates the appearance of ferromagnetism in ZnO. It increases the saturation magnetisation and decreases the critical amount of grain boundaries needed for FM. A drastic increase of the total solubility of dopants in ZnO with decreasing grain size has been also observed. It is explained by the multilayer grain boundary segregation.