Electrochemical cells or batteries featuring functional gradations, and having desirable, periodic configurations, and methods for making the same. One or more methods, in alone or in combination, are utilized to fabricate components of such electrochemical cells or batteries, which are designed to achieve certain thermal, mechanical, kinetic and spatial characteristics, and their effects, singly and in all possible combinations, on battery performance. The thermal characteristics relate to temperature distribution during charge and discharge processes. The kinetic characteristics relate to rate performance of the cells or batteries such as the ionic diffusion process and electron conduction. The mechanical characteristics relate to lifetime and efficiency of the cells or batteries such as the strength and moduli of the component materials. Finally, the spatial characteristics relate to the energy and power densities, stress and temperature mitigation mechanisms, and diffusion and conduction enhancements. The electrochemical cells or batteries constructed according to the methods presented in this invention are useful for all applications that require high rate performance, high energy/power density, good durability, high safety and long lifetime.