The science and technology of ferroelectric thin films is currently attracting worldwide attention because of its application to a new generation of novel devices. Prime, among these applications are nonvolatile ferroelectric random-access memories (NVFRAMs), which have high speed and extended endurance. The core of an NVFRAM is a capacitor with a ferroelectric film sandwiched between two electrode layers. The polarization of the ferroelectric layer in two possible opposite directions, upon application of an electric field between the two electrodes, provides the logic “1” and “0” states needed for binary-code memory. In spite of the advances in the science and technology of ferroelectric thin films and their integration into ferroelectric capacitors, some materials-related integration strategies as well as manufacturability issues have delayed commercialization of NVFRAMs. High-density memories require storage elements that approach submicron lateral dimensions. Thus, improved understanding of the materials properties and polarization phenomena is needed in conjunction with the development of new characterization tools that can enable such an understanding. For example, a fundamental issue in ferroelectric thin-film capacitors is the exact nature of the complex domain structure in the polarizable ferroelectric layer and its dynamics under high-speed switching conditions. The miniaturization of NVFRAMs requires understanding of granularity in polarization reversal dynamics, fatigue, and retention characteristics. In this respect, theoretical models and electrical measurements (e.g., polarization hysteresis loops and transient currents) have provided substantial insights into the nature of the switching processes. However, the models (phenomenological in nature) and the electrical measurements provide only a global or macroscopic view of the switching process.