Hydrogen peroxide (H2O2) has a wide range of important applications in various fields including chemical industry, environmental remediation, and sustainable energy conversion/storage. Nevertheless, the stark disconnect between today's huge market demand and the historical unsustainability of the currently-used industrial anthraquinone-based production process is promoting extensive research on the development of efficient, energy-saving and sustainable methods for H2O2 production. Among several sustainable strategies, H2O2 production via electrochemical and photochemical routes has shown particular appeal, because only water, O2, and solar energy/electricity are involved during the whole process. In the past few years, considerable efforts have been devoted to the development of advanced electrocatalysts and photocatalysts for efficient and scalable H2O2 production with high efficiency and stability. In this review, we compare and contrast the two distinct yet inherently closely linked catalytic processes, before we detail recent advances in the design, preparation, and applications of different H2O2 catalyst systems from the viewpoint of electrochemical and photochemical approaches. We close with a balanced perspective on remaining future scientific and technical challenges and opportunities.