The in situ formation of hydrogen peroxide, H2O2, is an attractive alternative to the current energy demanding and complex anthraquinone synthetic process. In this paper 2D materials, including graphene, graphitic carbon nitride (g-C3N4) and hexagonal boron nitride (hBN), are reviewed as electrocatalysts and photocatalysts for the selective two electron reduction of oxygen to give H2O2. Following an introduction to the complex oxygen reduction reaction, graphene is considered, followed by an account of g-C(3)N(4)and hBN in generating H2O2. It is readily evident that graphene combined with carbon-based supports, doped with N, B or BN, decorated with single atom catalysts and prepared as aerogels can be employed to enhance the production of H2O2. Although the mechanism of this two electron oxygen reduction reaction remains unclear, mildly oxidised graphene is more effective and this is fortunate as fully reduced graphene is difficult to form and maintain. While hBN and g-C(3)N(4)are much less studied as electrocatalysts, there is clear evidence that these 2D materials can be modified to give composites that favour the two electron oxygen reduction reaction, while g-C3N4-based materials are becoming well established as photocatalysts, effectively employing visible light, for the production of H2O2.