Bipolar membranes (BPMs), which consist of a cation-exchange layer (CEL) and an anion-exchange layer (AEL) sandwiching a thin dissociation catalyst layer (CL), present substantial promise for implementation in a sustainable future due to their ability to convert applied electrical energy into gradients in pH when operated in reverse bias (RB). This conversion of electrostatic potential into changes in pH is accomplished by driving the dissociation of water into protons (H+) and hydroxides (OH–) within the CL using the large electric fields (> 108 V m–1) present at that catalytic interface. The generated H+ and OH– can then transport out of the BPM through the CEL and AEL, respectively, to develop the pH gradient across the device. The ability to sustainably generate changes in pH via breakdown of the solvent water, without the need of added acid and base, is critical to many processes in electrochemical energy storage and conversion (e.g., water electrolysis, CO2 electrolysis), as well as environmental remediation (e.g., CO2 capture, wastewater treatment). When operated in forward bias (FB), BPMs have the capacity to recover voltage from the disparate sustained chemical environments enabled by the two oppositely charged polymers in a BPM. In FB, neutralization or recombination reactions occurring at the interface of the two polymers facilitates the flow of current. Unfortunately, the natures of electric field-enhanced water dissociation in RB and voltage recovery in FB are poorly understood, and there is great need to manage the transport of competing co- and counter- ions (e.g., (bi)carbonates, sodium, chloride, etc.) for all applications. In this dissertation, I will present the multi-scale physics of BPMs within an electrochemical engineering context and articulate design principles aimed at driving the development of advanced BPM devices. The chemistry, structure, and physics of BPMs are illustrated and related to the thermodynamics, transport phenomena, and chemical kinetics that dictate ionic and molecular fluxes and selectivity. I demonstrate how continuum modeling approaches can resolve and predict the fundamental physics and performance, respectively, of BPMs in model experimental systems. These continuum modeling approaches entail the discretization of BPM materials into control volumes in which the conservation equations (e.g., charge, mass, momentum, energy) are solved. I show that these continuum modeling approaches provide substantial insight into the mechanisms of transport and catalysis of BPMs operating both in the forward-bias mode, where voltage is recovered from gradients in pH, and the reverse-bias mode, where electrical potential is used to drive the generation of a pH gradient. Collectively, these fundamental analyses demonstrate the importance of multi-scale, multi-ion, and multi-component physics in dictating the electrochemical behavior and performance of BPMs for water dissociation and acid-base recombination. Finally, these continuum modeling approaches, and the fundamental understanding elucidated from these studies, are used to explore the implementation of BPMs in a variety of systems for energy storage and environmental remediation. BPMs in forward bias are considered for acid-base recombination batteries and CO2 electrolysis systems, and BPMs in reverse bias are considered for the conversion of bicarbonate to value-added products as well as direct air and ocean capture. Considering forward-bias BPMs for CO2 electrolysis highlights that while these materials are more energy efficient than their monopolar counterparts, they are not perfectly suited for mitigating crossover of carbon species due to the generation and crossover of neutral CO2 at the AEL|CEL interface. Designing asymmetric BPMs that encourage back-diffusion of CO2 are required to ameliorate the harmful crossover of CO2 through the membrane. When using forward-bias BPMs for acid-base recombination batteries developing polymers that are uniquely selective to OH– or H+, possibly through size-sieving, will be required to prevent mass-transport limitations in recombination associated with competition from other ionic impurities or redox species. Study of reverse-bias BPMs for bicarbonate conversion and carbon capture underscores the importance of localized pH swings generated by BPM water dissociation in controlling local bicarbonate-carbonate-CO2 equilibria that enables carbon capture and conversion. These works reveal that optimization of the physicochemical properties of the BPM and catalyst layers for these systems, along with efficient management of multi-phase phenomena (e.g., bubble formation) are key to making BPM processes energetically competitive with established thermal processes for carbon capture and conversion. Collectively, this dissertation demonstrates how the abilities of BPMs to control and extract energy from gradients in pH enables new approaches to energy conversion and environmental remediation. This dissertation also reveals the immense power of continuum modeling in understanding, optimizing, and controlling non-ideal, multi-component phenomena in these complex systems. These coupled interactions between species in the BPM give rise to emergent structure-property-performance relationships and tradeoffs, which yield design criteria for BPMs needed to achieve high permselectivity and voltaic efficiency. By connecting the fundamental physical phenomena in BPMs to device-level performance and engineering, I aim to facilitate the development of next-generation BPM devices for sustainable chemical processes.