Grain boundaries in high-$T_c$ superconductors

Since the first days of high-$T_{\mathrm{c}}$ superconductivity, the materials science and the physics of grain boundaries in superconducting compounds have developed into fascinating fields of research. Unique electronic properties, different from those of the grain boundaries in conventional metallic superconductors, have made grain boundaries formed by high-$T_{\mathrm{c}}$ cuprates important tools for basic science. They are moreover a key issue for electronic and large-scale applications of high-$T_{\mathrm{c}}$ superconductivity. The aim of this review is to give a summary of this broad and dynamic field. Starting with an introduction to grain boundaries and a discussion of the techniques established to prepare them individually and in a well-defined manner, the authors present their structure and transport properties. These provide the basis for a survey of the theoretical models developed to describe grain-boundary behavior. Following these discussions, the enormous impact of grain boundaries on fundamental studies is reviewed, as well as high-power and electronic device applications.