Paper, invented more than 2,000 years ago and widely used today in our everyday lives, is explored in this study as a platform for energy-storage devices by integration with 1D nanomaterials. Here, we show that commercially available paper can be made highly conductive with a sheet resistance as low as 1 ohm per square (Omega/sq) by using simple solution processes to achieve conformal coating of single-walled carbon nanotube (CNT) and silver nanowire films. Compared with plastics, paper substrates can dramatically improve film adhesion, greatly simplify the coating process, and significantly lower the cost. Supercapacitors based on CNT-conductive paper show excellent performance. When only CNT mass is considered, a specific capacitance of 200 F/g, a specific energy of 30-47 Watt-hour/kilogram (Wh/kg), a specific power of 200,000 W/kg, and a stable cycling life over 40,000 cycles are achieved. These values are much better than those of devices on other flat substrates, such as plastics. Even in a case in which the weight of all of the dead components is considered, a specific energy of 7.5 Wh/kg is achieved. In addition, this conductive paper can be used as an excellent lightweight current collector in lithium-ion batteries to replace the existing metallic counterparts. This work suggests that our conductive paper can be a highly scalable and low-cost solution for high-performance energy storage devices.