Electrochemical supercapacitors (ECs) have important applications in areas wherethe need for fast charging rates and high energy density intersect, including in hybrid and electric vehicles, consumer electronics, solar cell based devices, and other technologies. In contrast to carbon-based supercapacitors, where energy is stored in the electrochemical double-layer at the electrode/electrolyte interface, ECs involve reversible faradaic ion intercalation into the electrode material. However, this intercalation does not lead to phase change. As a result, ECs can be charged and discharged for thousands of cycles without loss of capacity. ECs based on hydrous ruthenia, RuO2·xH2O, exhibit some of the highest specific capacitances attained in real devices. Although RuO2 is too expensive for widespread practical use, chemists have long used it as a model material for investigating the fundamental mechanisms of electrochemical supercapacitance and heterogeneous catalysis. In this Account, we discuss progress in first-principles density-functional theory (DFT) based studies of the electronic structure, thermodynamics, and kinetics of hydrous and anhydrous RuO2. We find that DFT correctly reproduces the metallic character of the RuO2 band structure. In addition, electron-proton double-insertion into bulk RuO2 leads to the formation of a polar covalent O-H bond with a fractional increase of the Ru charge in delocalized d-band states by only 0.3 electrons. This is in slight conflict with the common assumption of a Ru valence change from Ru(4+) to Ru(3+). Using the prototype electrostatic ground state (PEGS) search method, we predict a crystalline RuOOH compound with a formation energy of only 0.15 eV per proton. The calculated voltage for the onset of bulk proton insertion in the dilute limit is only 0.1 V with respect to the reversible hydrogen electrode (RHE), in reasonable agreement with the 0.4 V threshold for a large diffusion-limited contribution measured experimentally. DFT calculations also predict that proton diffusion in RuO2 is hindered by a migration barrier of 0.8 eV, qualitatively explaining the observed strong charging rate-dependence of the diffusion-limited contribution. We found that reversible adsorption of up to 1.5 protons per Ru on the (110) surface contributes to the measured capacitive current at higher voltages. PEGS-derived models of the crystal structure of hydrated ruthenia show that incorporation of water in Ru vacancies or in bulk crystals is energetically much more costly than segregation of water molecules between slabs of crystalline RuO2. These results lend support to the so-called "water at grain boundaries" model for the structure of hydrous RuO2·xH2O. This occurs where metallic nanocrystals of RuO2 are separated by grain boundary regions filled with water molecules. Chemists have attributed the superior charge storage properties of hydrous ruthenia to the resulting composite structure. This facilitates fast electronic transport through the metallic RuO2 nanocrystals and fast protonic transport through the regions of structural water at grain boundaries.