Heterogeneous hydrogenation catalysis (HHC) is a promising advanced reductive process for treating oxidizing contaminants in drinking water including oxoanions such as nitrate and nitrite. HHC has yet to be implemented at large scales due to challenges regarding reactor design and catalyst cost. The overarching goal of this dissertation was to develop the Catalytic Hydrogel Membrane Reactor (CHMR), an interfacial membrane reactor for HHC that allows for high activity in a continuous flow reactor. The CHMR consists of a central, gas permeable, tubular hollow-fiber membrane (HFM), the exterior of which is coated with a highly aqueous Ca-alginate hydrogel that serves as a support matrix for embedded catalytic Pd nanoparticles that can drive catalytic reduction of oxidized contaminants by H2. Primary research objectives of this work were to (1) develop a structurally stable and catalytically active CHMR and demonstrate its efficacy for hydrogenation reactions, (2) evaluate the effect of water quality and operational parameters including reactive species concentration, pH, co-occurring aqueous species, and gas delivery mode on catalytic activity and hydrogel stability, and (3) develop a 1-D model of the CHMR to predict the effect of reaction conditions and reactor configuration on catalytic performance and optimize the reactor design for catalytic activity and contaminant conversion. Results show that the CHMR effectively reduced the selected model contaminant, nitrite (NO2-), when operated in a continuous flow configuration. The interfacial nature of H2 and NO2- delivery to catalyst active sites allowed for excellent control of reaction conditions for optimization of catalytic activity and byproduct selectivity. Maximum catalytic activity for NO2- hydrogenation in the CHMR (1.87 L mol-Pd-1 s-1, 2.49 x 10-3 mol-N mol-Pd-1 s-1) was comparable to alternative immobilized catalyst reactors. Mass-transfer limitations on catalytic activity were minimized by the excellent effective diffusivity of aqueous species within the hydrogel and the hydrogel showed excellent stability to typical groundwater conditions. Development of a 1-D model of the CHMR demonstrated the potential for further enhancing activity of the CHMR by optimization of hydrogel properties. These results show that CHMRs are a promising class of interfacial catalytic membrane reactor that deserves further investigation.