The bicontinuous cubic (Q) lyotropic liquid crystal (LLC) phases formed by the phase-separation and self-organization of amphiphilic molecules in water are intriguing structures for a number of transport-related applications because they possess ordered, uniform, 3D-interconnected water channels on the size of single molecules. Polymeric materials formed from either the templated polymerization or cross-linking of conventional monomers around Q phases, or the direct polymerization or cross-linking of Q phases formed by reactive amphiphiles retain the desired LLC nanostructure but are more robust for true application development. The structures of Q LLC phases were only elucidated in the late 1980s, and the first successful preparation of polymers based on Q phases was reported soon after. However, the development and demonstration of these nanoporous polymers for material applications were not realized until the first decade of the twenty-first century. This focus review provides an overview of work in the area of Q LLC phase-based polymer materials, with a focus on the work of our research group and that of our collaborators on polymer networks prepared by the direct polymerization of reactive Q phases and their development as functional materials for several engineering applications. Keywords: bicontinuous cubic; liquid crystal; lyotropic; nanoporous; polymer INTRODUCTION Lyotropic liquid crystals (LLCs) are amphiphilic molecules typically composed of a hydrophilic headgroup section and a hydrophobic tail section that have the ability to phase-separate and self-organize into nanostructured assemblies in the presence of water. The resulting fluid, ordered LLC phases have varying degrees of average order, different levels of hydrophilic and hydrophobic domain interconnectivity, and uniform periodic features in the circa 1-10 nm size range (For general reviews on LLC phases and their classifications, see: refs 1-3). LLC phases have recently attracted a great deal of attention because of their benefits as a versatile platform for the design of functional, nanoporous polymer materials. For example, by employing reactive LLCs (that is, monomers), the desired phase can be locked-in directly via chemical cross-linking to afford robust, nanoporous polymer networks (For reviews on the synthesis and applications of nanostructured polymers made from polymerizable LLCs, see: refs 4-6). LLC networks made by this approach have been used for applications such as templated nanocomposite synthesis, drug delivery, molecular transport/separation and heterogeneous catalysis. 7,8 Alternatively, non-polymerizable LLC phases have been used as nanostructured templates for the polymerization of conventional monomers dissolved in either the hydrophilic or hydrophobic domains. Subsequent