Burgeoning energy and water scarcity challenges motivate the development of new membrane materials for charge transport as well as chemical and water separations. This in turn requires an improved understanding of the physics that govern charged and uncharged solute transport in membranes, and particularly the motion of such species in nm-scale confinement in polymeric materials. This dissertation addresses transport in porous polymers with highly ordered nm-scale constrictions made from lyotropically assembled surfactant mesophases. The primary concerns of the thesis include the extent to which one can control the bulk material properties of a polymerized lyotropic mesophase and the bulk and dynamic pictures of transport in the resulting nanoconfined spaces. The explored polymers have controlled dimensions, curvature, and solid volumes, allowing for discussion and alteration of the membrane’s internal environment. Fine control over the mesophase geometry is shown through a study incorporating a spiropyran dopant into a bicontinuous gyroid, where pore size is actively reduced by 5 % in response to stimuli, lowering acid vapor flux by 30 %. Membrane tensile properties are altered by adjustment of crosslinking groups in a similar bicontinuous gyroid mesophase. By optimizing the number of -diene crosslinking groups, improvements in tensile strength are found in comparison to the original polymer. Anion conductivities of two differing morphologies, the Ia3d gyroid and HI cylinders, are investigated, with a focus on determining differences in bulk properties based on morphology, anion identity, and conditions such as temperature and relative humidity. Potassium ion transport through another lyotropically self-assembled mesophase is performed and deemed a suitable candidate for further study. The self-assembled materials presented in this dissertation are found to be resilient, with higher conductivity than previously reported ordered polymeric electrolytes. Solvent composition is found to be a first order effect on conductivity, and anion identity shows that nanoconfinement enhances differences in diffusivity due to solvation shell depletion and condensed charge pair formation. Additional work varying relative humidity and pore size unites bulk activation energies and conductivities with short-time dynamic phenomena. These findings motivate future work in understanding the dynamics of these systems and putting these porous polymers into useful scenarios.