Although traditional materials discovery has historically benefited from intuition-driven experimental approaches and serendipity, computational strategies have risen in prominence and proven to be a powerful complement to experiments in the modern materials research environment. It is illustrated here how one may harness a rational co-design approach-involving synergies between high-throughput computational screening and experimental synthesis and testing-with the example of polymer dielectrics design for electrostatic energy storage applications. Recent co-design efforts that can potentially enable going beyond present-day "standard" polymer dielectrics (such as biaxially oriented polypropylene) are highlighted. These efforts have led to the identification of several new organic polymer dielectrics within known generic polymer subclasses (e.g., polyurea, polythiourea, polyimide), and the recognition of the untapped potential inherent in entirely new and unanticipated chemical subspaces offered by organometallic polymers. The challenges that remain and the need for additional methodological developments necessary to further strengthen the co-design concept are then presented.