Three-dimensional battery architectures offer a new approach for powering autonomous microsystems that serve such application areas as sensing/actuation, communication and health monitoring. With 3-D battery architectures, one exploits the third dimension, height, to increase the amount of electrode material within a given footprint area. Moreover, by using 3-D electrode designs which minimize the ionic path length between electrodes, there is the prospect of achieving high energy and power density within the small footprint area. The present paper reviews recent advances in the development of 3-D lithium-ion battery architectures which incorporate periodic electrode arrays. The defining characteristic of 3D battery designs is that transport between electrodes remains one-dimensional (or nearly so) at the microscopic level, while the electrodes are configured in non-planar geometries. The design rules developed for 3D battery architectures indicate that it is possible to achieve both high energy density and high power density within a small footprint area. These properties are particularly important for integrated microsystems where the available area for the power source is limited to millimeter dimensions. The present paper reviews recent advances in the development of 3D microbatteries which are based on using periodic electrode arrays.