In the first part of the talk, I will tell you about the controversy about the position of the defect levels for the oxygen vacancy in ZnO and how we tried to resolve it. In the second part, I will discuss the case of nitrogen in ZnO. I will discuss why nitrogen on an oxygen site forms a deep rather than shallow acceptor level. However, it is known that there exists a shallow level related to nitrogen doping. The question is then what defect complex is responsible for this shallow level? I will try to convince you that a N2 molecule located on a Zn-site has all the expected behavior of a shallow acceptor. Furthermore, the N2 on Zn model explains the g-factor and hyperfine interaction of a known EPR center in ZnO. Finally, I will discuss how N2 may get preferentially incorporated on a Zn polar rather than O polar surface.