The systematic design of structurally precise polymer systems is an elusive materials science goal. Here, I will describe recent efforts using dynamic bonding, supramolecular interactions, and non-covalent templation to prepare two-dimensional macromolecular sheets as single-crystals and high-quality films, both of which are ideal for property and device measurements. I will also briefly elaborate on how these insights enabled the preparation of synthetic one-dimensional nanotubes. Another approach to understanding structurally defined polymers relies on measuring single-polymer chains at the nanoscale limit. To this end, I will discuss how using a scanning tunneling microscopy break-junction technique, the unique electronic properties of open-shell radicaloids can be studied at the single-polymer limit. Throughout these discussions, I will highlight how structurally defined polymers, when combined with advanced processing and measurement strategies, yield emergent combinations of thermal, mechanical, optical, and electronic properties not available in other material platforms.