Block copolymers (BCPs) have been indispensable building blocks to create a range of soft nanostructures including discrete particulates (micelles and vesicles) and periodic structures via spontaneous assembly in bulk and in solution. The size, shape, and phase of these structures can be controlled by the rational design of the molecular structure of building blocks based on the structural analogy of BCPs to lipids and small molecule surfactants. Inverse bicontinuous cubic mesophases of polymers, or polymer cubosomes when in colloidal forms, are emerging nanostructures composed of triply periodic minimal surfaces (TPMSs) of block copolymer bilayers. Created by spontaneous assembly of BCPs in solution, polymer cubosomes internalize two nonintersecting nanochannel networks arranged in a cubic crystalline order. As well-defined porous particles with highly ordered internal structures and high surface-area-to-volume ratios, polymer cubosomes can be used for chemical reactors or bioreactors, carriers capable of cargo loading and release, and scaffolds for nanotemplating. However, despite their structural similarity to lipid cubosomes and applicability, polymer cubosomes have been only sporadically observed as an outcome of serendipity until recent studies demonstrated that BCPs could form well-defined polymer cubosomes in solution.In this Account, we describe our recent progress in creating polymer cubic mesophases and their colloidal particles (polymer cubosomes) in dilute solution. BCPs with nonlinear architectures (dendritic-linear, branched-linear, and branched-branched BCPs) preferentially self-assembled to inverse mesophases in solution when the block ratio (f), defined as a molecular weight ratio of the hydrophilic block to that of the hydrophobic block, was small (<10%). The resulting lyotropic structures transformed from flat bilayers to cubic phases of primitive cubic and double diamond lattices and finally to inverted hexagonal phases as f decreased. We proposed that the architecture of a BCP plays an important role in the preferential formation of polymer cubosomes in solution. The presence of the bulky hydrophilic block limited chain stretching of the hydrophobic polymer block, which would increase the packing parameter of the BCP to greater than unity, a prerequisite for inverse mesophase formation. The structural characteristics of polymer cubosomes, such as lattice symmetries, pore sizes, and lattice parameters, could also be controlled by fine-tuning the structural parameters of BCPs. We also suggested nonsynthetic methods to precisely control the phase and internal lattice of inverse mesophases of BCPs by the coassembly of two BCPs with different block ratios (mix-and-match approach) and the modulation of the affinity of the common solvent toward the hydrophobic block of the BCP. To investigate the potential applications of polymer cubosomes, we prepared inorganic photonic crystals using a cubosome-templated synthesis. We also discussed the utilization of cubosomes as chemical reactors by functionalization of the surface and the covalent stabilization of transient self-assembled structures via cross-linking of the hydrophobic domain. This Account reflects the efforts of synthetic chemists to understand the self-assembly behavior of BCPs to form complex morphologies in solution. We hope that our Account inspires efforts from chemists and other scientists to further understand these structures with infinite mazes of complexity and possibility.