We show that oxidation of phosphorene can lead to the formation of a new family of planar (two-dimensional) and tubular (one-dimensional) oxides and suboxides, most of them insulating. This confers to black phosphorus a native oxide that can be used as barrier material and protective layer. Furthermore, the bandgap of phosphorene oxides depends on the oxygen concentration, suggesting that controlled oxidation can be used as a means to engineer the bandgap. For the oxygen saturated composition, , both the planar and tubular phases have a large bandgap energy of about 8.5 eV and are transparent in the near UV. These two forms of phosphorene oxides are predicted to have the same formation enthalpy as , the most stable of the previously known forms of phosphorus pentoxide.