<p>We review our recent work on the thermal conductivity of polymers that examines changes in conductivity that are produced by systematic variations in molecular structure, density, and crystallinity. Our interests are in exploring both the lower and upper limits of the isotropic thermal conductivity in polymers that are relatively simple to synthesize and process. Our recent work emphasizes (i) low and high thermal conductivity in epoxies synthesized from diepoxides and diamines; (ii) amorphous and semicrystalline polyesters; and (iii) the lower limit to thermal conductivity that we can achieve in polyurethane chemistry, i.e., reactions of polyols and isocyanates. For each system, we strive to fully characterize the thermal conductivity, heat capacity, density, coefficient of thermal expansion, longitudinal modulus, vibrational spectra by vibrational spectroscopy, and microstructure via X-ray scattering. Our data for epoxies, polyesters, and polyurethanes provide a baseline for the design of polymeric materials with reduced and enhanced thermal conductivity.</p> Graphical abstract <p></p>