  The ongoing scientific interest in the properties and structure of electric
double layers (EDLs) stems from their pivotal role in (super)capacitive energy
storage, energy harvesting, and water treatment technologies. Classical density
functional theory (DFT) is a promising framework for the study of the in- and
out-of-plane structural properties of double layers. Supported by molecular
dynamics simulations, we demonstrate the adequate performance of DFT for
analyzing charge layering in the EDL perpendicular to the electrodes. We
discuss charge storage and capacitance of the EDL and the impact of screening
due to dielectric solvents. We further calculate, for the first time, the
in-plane structure of the EDL within the framework of DFT. While our
out-of-plane results already hint at structural in-plane transitions inside the
EDL, which have been observed recently in simulations and experiments, our DFT
approach performs poorly in predicting in-plane structure in comparison to
simulations. However, our findings isolate fundamental issues in the
theoretical description of the EDL within the primitive model and point towards
limitations in the performance of DFT in describing the out-of-plane structure
of the EDL at high concentrations and potentials.
