Streams and rivers are a vital part of our ecosystem. They are imperiled by human ecological activities such as urbanization, industrialization, and agriculture which discharge excess nitrate and other pollutants into our waterways. Here, this dissertation seeks to understand the physical and biogeochemical processes which attenuate pollutants in stream corridors. The focus is hyporheic zones which form the interface between surface water and groundwater below and adjacent to stream channels, and riparian zones which form the interface between channels and adjacent uplands, both of which can attenuate pollutants. In this context, soil-pipes can dominate subsurface hydraulics. This research first employed MODFLOW and MT3D-USGS to model transient hyporheic hydraulics and nitrate transport in a length of riparian/riverbank soil to probe the effects of soil pipes on hydraulics and denitrification due to peak flow events in the channel. Findings showed that inserting just one soil pipe 1.5 m in length caused a ~75% increase in both hyporheic exchange and denitrification. A rough upscaling showed soil pipes could remove up to ~3% of nitrate along a 1-km reach. Next, the ability of soil pipes to bypass the often championed ability of riparian buffers to remove nitrate migrating from uplands to the channel was evaluated. This effort also employed MODFLOW and MT3D-USGS to simulated hydraulics and nitrate removal along a length of riparian soil. Findings showed that soil pipes increased flow of nitrate to the banks by five orders of magnitude in some cases. We posited a non-dimension parameter which governs when nitrate bypass is significant. In addition to soil pipes, dune bedforms can also enhance hyporheic exchange, primarily in the stream/riverbed. Again employing MODFLOW but now pairing with the transport code SEAM3D to simulate microbially-mediated aerobic metabolism of dissolved organic carbon and dissolved oxygen, the combined effects of dune translation and microbial growth and death were explored. Major findings include that neglecting microbial growth can lead to inaccurate modeling of biogeochemistry, and that aerobic metabolism increased with celerity. The results herein bolster knowledge of natural pollutant attenuation in stream and river corridors, and have implications for pollutant mitigation strategy and stream credit allocation.