The metal-electrolyte interface is prototypical in electrochemistry and highly relevant for energy storage, conversion and corrosion processes. In the boundary region between metal electrode and electrolyte solution, an electric double layer (EDL) is formed when the excess electronic charge on the metal surface is compensated by equal and opposite ionic charge in electrolyte solution. This happens when the system is outside of so-called the potential of zero charge (PZC). Despite of decades of efforts, EDLs at the metal-electrolyte interfaces are still full of surprises. This is evidenced by recent experimental reports of a strong deviation from the Gouy-Chapman theory for the diffuse double layer, an unexpected high capacitance of the metal nanoparticle-water interfaces, and different ionic responses from Na + and Cl -shown in the absorption THz spectra. Understanding the molecular structure of EDLs at the metal-electrolyte interface requires inputs from theoretical investigations. Molecular modelling built on the principle of quantum mechanics and statistical mechanics are most suitable to unveil the factors that contribute to the double-layer structures and their effects on electrochemical activity. Significant progress in this area has been made recently, which points out the importance of water dynamics, the chemisorption of water, and specific ion adsorptions. Nevertheless, a direct computation of the Helmholtz capacitance of electrified metal-electrolyte interfaces which is a key experimental observable is not fully available from first-principles-based molecular dynamics simulations.