The search for new redox-active organic materials (ROMs) is essential for the development of sustainable energy-storage solutions. In this study, we present a new class of cyclobuta[b]quinoxaline-1,2-diones or squaric acid quinoxalines (SQXs) as highly promising candidates for ROMs featuring exceptional stability and high redox potentials. While simple 1,2- and 1,3-squaric acid amides (SQAs), initially reported by Hünig and coworkers decades ago, turned out to exhibit low stability in their radical cation oxidation states, we demonstrate that embedding the nitrogen atoms into a quinoxaline heterocycle leads to robust two-electron SQX redox systems. A series of SQX compounds, as well as their corresponding radical cations, were prepared and fully characterized, including EPR spectroscopy, UV-vis spectroscopy, and X-ray diffraction. Based on the promising electrochemical properties and high stability of the new ROM, we developed SQX-functionalized polymers and investigated their physical and electrochemical properties for energy-storage applications. These polymers showed remarkable thermal stability well above 200 °C with reversible redox properties and potentials of about 3.6 V vs Li+/Li. By testing the galvanostatic cycling performance in half-cells with lithium-metal counter electrodes, a styrene-based polymer with SQX redox side groups showed stable cycling for single-electron oxidation for more than 100 cycles. These findings render this new class of redox-active polymers as highly promising materials for future energy-storage applications.