Monte Carlo and molecular dynamics simulations on pure water and aqueous electrolyte solutions exposed to a strong external electric field were used to model the electrospinning process from the free liquid surface, with the goal of assessing their potential to gain insight into the molecular-level mechanisms underlying the process. Three regimes involved in the electrospinning process the free liquid surface, the apex of the Taylor cone, and the erupting jet were selected for simulation using three different strategies. All simulations provide the same qualitative picture and exhibit scenarios consistent with experimental observations. It is found that ions play only a rather secondary role, in the sense that the process is driven by the water molecules. The strong electric field near the tip of the Taylor cone initially arranges the water molecules, creating an embryo of a jet into which the ions subsequently enter. At high concentrations, the ions can destabilize the jet, leading to electrospraying. At low electrolyte concentration, the embryo grows, leading to a stable jet and potentially to generation of a meso-/macroscopic fiber.