High power miniature power sources could enable new microelectronic systems, but performance and integration remain a challenge. We report lithium ion microbatteries having power densities up to 7.4 mW/cm2'm, which equals or exceeds that of the best supercapacitors, and which is 2,000 times higher than that of other microbatteries. The battery microarchitecture optimizes ion and electron transport for high power density while maintaining a high volume of active material for high energy density. The architecture consists of three-dimensional bicontinuous interdigitated microelectrodes and can be scaled to larger sizes without sacrificing power and energy density..