Here, we describe the design features that lead to intrinsically thermally conductive polymers. Though polymers are conventionally assumed to be thermal insulators (<0.3 W m-1 K-1), significant efforts by the thermal transport community have shown that polymers can be intrinsically thermally conductive (>1.0 W m-1 K-1). However, these findings have not yet driven comprehensive synthetic efforts to expose how different macromolecular features impact thermal conductivity. Preliminary theoretical and experimental investigations have revealed that high k polymers can be realized by enhancing the alignment, crystallinity, and intermolecular interactions. While a holistic mechanistic framework does not yet exist for thermal transport in polymeric materials, contemporary literature suggests that phonon-like heat carriers may be operative in macromolecules that meet the abovementioned criteria. In this review, we offer a perspective on how high thermal conductivity polymers can be systematically engineered from this understanding. Reports for several classes of macromolecules, including linear polymers, network polymers, liquid-crystalline polymers, and two-dimensional polymers substantiate the design principles we propose. Throughout this work, we offer opportunities for continued fundamental and technological development of polymers with high thermal conductivity.