We theoretically discuss here the relationships between the structure of recently synthesized nanorings, dubbed as cyclo-2,7-pyrenylene (CPY) and formed upon bending and bonding a finite number of pyrene units until self-cyclation, and a set of chemically relevant properties such as the induced structural and energetical strain, the electronic and optical properties, or the response to charge injection, as well as their transport mechanism through a concerted migration of charge-carriers. We also compare these properties, and their evolution with the number of pyrene-linked units, with those obtained for the closely related cycloparaphenylene (CPP) compounds, trying to disclose the underlying structure-property guidelines. To do it, we always employ dispersion-corrected DFT methods to systematically include the key effects affecting all the properties tackled. A correct match with some available experimental results, for the [4]CPY compound (the only one synthesized so far), anticipates the accuracy of the calculations done for the rest of compounds. Finally, since this kind of systems are envisioned as possible precursors for the fine-tuned and controlled synthesis of carbon nanotubes, we also address the stability of the dimers found in their crystalline structure, and the associated cohesive energy, which may drive the synthesis of the corresponding nanotubes after an adequate dehydrogenation reaction.