Using first-principles simulations, we identify the microscopic origin of the nonlinear dielectric response and high energy density of polyvinylidene-fluoride-based polymers as a cooperative transition path that connects nonpolar and polar phases of the system. This path explores a complex torsional and rotational manifold and is thermodynamically and kinetically accessible at relatively low temperatures. Furthermore, the introduction of suitable copolymers significantly alters the energy barriers between phases providing tunability of both the energy density and the critical fields. DOI: 10.1103/PhysRevLett.108.087802 PACS numbers: 61.41.+e, 71.15.Nc, 77.22.Àd The usual means of storing electrical energy are either batteries, where the current induces chemical reactions, or capacitors, where especially chosen dielectrics enhance the stored energy. Current batteries offer energy densities of about 10 2 -10 3 Wh=kg, but their power densities, i.e., the speeds at which they can be discharged, are only 50-300 W=kg [1]. Fuel cells have energy densities [1] several times larger than batteries, but their power densities are significantly lower. Conventional capacitors have energy densities of only $0:05 Wh=kg, but their power densities reach 10 5 W=kg and they can be fully discharged over 10 6 times, compared to 200-1000 times for batteries. They can thus be used to release or store quick bursts of energy, e.g., in acceleration or regenerative breaking. Ultracapacitors, or electric double-layer capacitors, occupy a middle ground in energy storage. They achieve energy densities of $10 Wh=kg and power densities of $10 3 W=kg [1] by using porous plates suspended in an electrolyte to attract negative or positive ions to the positive or negative electrodes, thereby dramatically shrinking the distance between the positive and negative "layers." This increases the capacitance per unit area, c ¼ " 0 K=d, where K is the dielectric permittivity and d is the distance between capacitor plates. However, the charge-discharge speeds of ultracapacitors are limited by ion diffusion in the electrolyte, while the porosity of the plates leads to small breakdown voltages within each cell. In contrast, by using ultrafast phase transitions as the primary mechanism of energy storage, polyvinylidene-fluoride (PVDF)-based capacitors reach the power densities and breakdown fields of conventional capacitors, while their energy densities are 10 2 -10 3 larger, potentially rivalling those of ultracapacitors.In traditional capacitors, the stored energy density is given by U ¼ 1=2" 0 KE 2 b , where E b is the electric breakdown field. Enhancement of K and/or E b leads to increased energy storage. However, both are native properties that are constants for any chosen material. High K materials such as ferroelectric oxides have low E b . Polymers typically have high E b but very small K. Materials that have both high K and high E b have not yet been found and attempts to create composites with the same characteristics have not yet met with success....