ConspectusRecently, supramolecular polymers (SPs), which depend on the formation of reversible bonds between monomers, have attracted attention as a class of materials that can overcome the potential environmental problems of conventional polymeric materials. The development of various supramolecular polymers is important not only for their direct application as materials but also because their unique polymerization processes and dynamic properties have a profound influence on the development of polymeric and small-molecule-based functional materials. In other words, by limiting the dimensionality of molecular assemblies to one dimension, we can discover the essential aspects of self-assembly and self-organization. In particular, supramolecular polymerization, in which π-electron-rich planar molecules are stacked one-dimensionally via multiple interactions, is interesting because it gives “π-stacked SPs” with one-dimensional crystal-like order. The excellent intrinsic (internal) structural order of π-stacked SPs is difficult to observe in higher-order structures that exhibit only a monotonous linear structure. However, our research has shown that when internal structural order intrinsically generates curvature, the curvature appears as a major feature of the entire polymer chain. This intrinsic curvature allows the formation of diverse topologies such as toroids, random coils, waves, spirals, and helicoids using π-stacked SPs and also allows structural changes at the single-polymer-chain level along a topology-dependent energy landscape. In other words, π-stacked SP-based nanomaterials could enable free control of the structure at the single-polymer-chain level. This Account will focus on our research into curved supramolecular polymers (CSPs) during the last five years. CSPs are formed by the hydrogen bonding between barbiturate-containing π-conjugated molecules to produce giant supramolecular monomers. We first give an overview of the molecular design of the monomers required for the formation of CSPs, the unique energy landscape of CSPs, and their evaluation and analysis methods, before describing the four specific properties of CSPs. The first is structural controllability via the introduction of photoresponsive units such as azobenzene and diarylethene moieties. The isomerization of these photochromic molecules within the CSP main chain has a local effect on the curvature and allows photocontrol of their entire topology. The second is the copolymerization of different molecules via the formation of rosettes. Here, two extreme examples, block and alternating copolymerization, are discussed. Third, we describe a structural transition that involves the rearrangement of hydrogen bonds. This is a new property, which enables a structural transition from a soft and highly soluble supramolecular polymer to a hard and poorly soluble crystalline structure and thus expands the applicability of CSPs to environmentally important and electronic materials. Finally, self-assembled polycatenanes are described as an example of an entirely new “topological self-organization” using CSP formation on CSP surfaces, i.e., secondary nucleation. This work is also a turning point in our CSP research and includes concepts that are broadly applicable to the creation of self-organized functional materials. At the end of this Account, we will discuss how CSPs can contribute to nanotechnology or mesotechnology as single-chain-polymer materials. We hope that the landscape depicted in this Account will guide the development of a variety of new functional materials.