The transport and structure of room-temperature ionic liquids (RTILs) in conical nanopores under external electric fields were studied using molecular dynamics simulations. Electrically neutral, nonuniformly charged, and uniformly charged nanopores were considered. The current-voltage relationship was calculated as the macroscopic transport property. When the magnitude of the applied voltage increases, the magnitude of the current was found to increase nonlinearly with an increasing slope. The nonlinearity was traced back to that the RTILs' electrical conductivity increases as the magnitude of the electric field increases and as the ion concentration decreases (ion depletion) because of the solvent-free nature of the RTILs. The degree of ion depletion is highest near the pore tip, and it decreases as the location moves from the tip to the base, because the electric field is strongest near the tip while RTILs are more bulk-like near the base and their conductivities' dependence on the electric field is weaker than that near the tip. At the same applied voltage, the current through the nonuniformly charged pore was weaker than that through the neutral pore, while the current through the uniformly charged pore was stronger. This is because the hindered transport due to the higher total ion concentration and the lower degree of ion depletion dominates in the nonuniform case, while the enhanced transport due to the formation of electrical double layers (EDLs) dominates in the uniform case. Cation and anion currents were calculated separately, and the results show that negatively charged nanopores are cation-selective. EDLs were observed near pore walls due to the external electric field and surface charges, and the results suggest that the ion density in EDLs is tunable by varying the applied voltage across the system. The physical insights provided in this study demonstrate the importance of solvent-free nature and strong ion-ion correlations in RTILs on their nonequilibrium transport and structures in nanopores, and the results imply that the charging dynamics of RTILs in nanoporous electrodes in supercapacitor and energy applications could be greatly enhanced under larger applied voltages.