Micro-supercapacitors are promising energy storage devices that can complement or even replace batteries in miniaturized portable electronics and microelectromechanical systems. Their main limitation, however, is the low volumetric energy density when compared with batteries. Here, we describe a hierarchically structured carbon microfibre made of an interconnected network of aligned single-walled carbon nanotubes with interposed nitrogen-doped reduced graphene oxide sheets. The nanomaterials form mesoporous structures of large specific surface area (396 m(2) g(-1)) and high electrical conductivity (102 S cm(-1)). We develop a scalable method to continuously produce the fibres using a silica capillary column functioning as a hydrothermal microreactor. The resultant fibres show a specific volumetric capacity as high as 305 F cm(-3) in sulphuric acid (measured at 73.5 mA cm(-3) in a three-electrode cell) or 300 F cm(-3) in polyvinyl alcohol (PVA)/H(3)PO(4) electrolyte (measured at 26.7 mA cm(-3) in a two-electrode cell). A full micro-supercapacitor with PVA/H(3)PO(4) gel electrolyte, free from binder, current collector and separator, has a volumetric energy density of ∼6.3 mWh cm(-3) (a value comparable to that of 4 V-500 µAh thin-film lithium batteries) while maintaining a power density more than two orders of magnitude higher than that of batteries, as well as a long cycle life. To demonstrate that our fibre-based, all-solid-state micro-supercapacitors can be easily integrated into miniaturized flexible devices, we use them to power an ultraviolet photodetector and a light-emitting diode.