Electrical double layer capacitors (EDLCs), or supercapacitors, continue to gain an increasing attention as promising electrical energy storage devices that store energy via the accumulation of ions in a nanometer-thick layer at electrochemically-stable high specific surface area active electrodes. A notable improvement in EDLC performance has been achieved due to recent advances in understanding charge storage mechanisms, development of advanced nanostructured electrodes and electrochemically stable electrolytes such as room temperature ionic liquids. Despite extensive experimental work on these systems, the specifics of what happens inside and on the surfaces of nanostructured electrodes are still not well understood. In this presentation, I will discuss the results of our latest molecular dynamics simulations using state-of-the-art methodologies and focusing on gaining insight into understanding the molecular level phenomena that influence EDLC performance. Specifically, the presentation will focus on: a) the complex dependence of the capacitance on electrolyte double layer structure, electrode voltage and polarity, b) the influence of surface topography and nanopore dimensions/morphology on the charge storage mechanisms, and c) the issues associated with ion dynamics in charged nanostructures. The obtained molecular simulations results are discussed in light of reported experimental data and observations.