ZnO typifies a class of materials that can be doped via native defects in only one way: either n type or p type. We explain this asymmetry in ZnO via a study of its intrinsic defect physics, including Zn-O, Zn-i, V-O, O-i, and V-Zn and n-type impurity dopants, Al and F. We find that ZnO is n type at Zn-rich conditions. This is because (i) the Zn interstitial, Zn-i, is a shallow, donor, supplying electrons; (ii) its formation enthalpy is low for both Zn-rich and O-rich conditions, so this defect is abundant; and (iii) the native defects that could compensate the n-type doping effect of Zn-i (interstitial O, O-i, and Zn vacancy, V-Zn), have high formation enthalpies for Zn-rich conditions, so these "electron killers" are not abundant. We find that ZnO cannot be doped p type via native defects (O-i, V-Zn) despite the fact that they are shallow (i.e., supplying holes at room temperature). This is because at both Zn-rich and O-rich conditions, the defects that could compensate p-type doping (V-O, Zn-i, Zn-O) have low formation enthalpies so these "hole killers" form readily. Furthermore, we identify electron-hole radiative recombination at the V-O center as the source of the green luminescence. In contrast, a large structural relaxation of the same center upon double hole capture leads to slow electron-hole recombination (either radiative or nonradiative) responsible for the slow decay of photoconductivity.