Although often thought of as an area of low technology that is stagnant and uninteresting in the past, the use of electrochemical cells for energy storage and conversion purposes has received greatly increased attention recently. There are two general directions of interest. One is the long term goal of the development of electrical propulsion for vehicles, and the other is the rapid growth of portable electronic devices that require power sources with maximum energy content and the lowest possible size and weight. Most of the activities have been aimed at the development of electrochemical cells that are optimized toward either maximum specific energy or energy density. On the other hand, some of the current applications require electrical energy at high power levels for short times. These include very short pulses for digital electronic devices, the somewhat longer power pulse demands of some implantable medical devices, and the much larger transient power needs in connection with vehicle traction. Several mechanisms can be used to provide short term energy, and they have fundamentally different characteristics, and thus are potentially applicable to different types of transient output requirements. Some of these provide behavior that is analogous to an electrical capacitor, whereas others have more the character of batteries. The several electrochemical methods that can be used to evaluate the critical materials parameters in materials that might be applicable to such applications are discussed, as well as the use of LaPlace transform methods to convert information about the physical mechanisms and parameters of individual components into the dynamic response of an electrochemical system.