Oxyanions, such as nitrate, perchlorate, selenate, and chromate are commonly occurring contaminants in groundwater, as well as municipal, industrial, and mining wastewaters. Microorganism-mediated reduction is an effective means to remove oxyanions from water by transforming oxyanions into harmless and/or immobilized forms. To carry out microbial reduction, bacteria require a source of electrons, called the electron-donor substrate. Compared to organic electron donors, H2 is not toxic, generates minimal secondary contamination, and can be readily obtained in a variety of ways at reasonable cost. However, the application of H2 through conventional delivery methods, such as bubbling, is untenable due to H2's low water solubility and combustibility. In this review, we describe the membrane biofilm reactor (MBfR), which is a technological breakthrough that makes H2 delivery to microorganisms efficient, reliable, and safe. The MBfR features non-porous gas-transfer membranes through which bubbleless H2 is delivered on-demand to a microbial biofilm that develops naturally on the outer surface of the membranes. The membranes serve as an active substratum for a microbial biofilm able to biologically reduce oxyanions in the water. We review the development of the MBfR technology from bench, to pilot, and to commercial scales, and we elucidate the mechanisms that control MBfR performance, particularly including methods for managing the biofilm's structure and function. We also give examples of MBfR performance for cases of treating single and co-occurring oxyanions in different types of contaminated water. In summary, the MBfR is an effective and reliable technology for removing oxyanion contaminants by accurately providing a biofilm with bubbleless H2 on demand. Controlling the H2 supply in accordance to oxyanion surface loading and managing the accumulation and activity of biofilm are the keys for process success.