Semiconductor nanostructures are a field of enormous and still-growing research interest. On one hand, they are already realized in mass products, e.g., in high-electron-mobility field-effect transistors and quantum-well lasers. On the other hand, they allow, in specially tailored systems, the investigation of fundamental properties, such as many-particle interactions of electrons in reduced dimensions. This book attempts to fill the gap between general semiconductor textbooks and research articles. It provides (i) an introduction into the basic concepts of inelastic light scattering on semiconductor nanostructures and into their fabrication and basic properties, and, (ii) a description of the most striking recent advances in this field. Each chapter is as self-contained as possible. The monograph should interest researchers, experimentalists as well as theorists, and research students working in the field. It should also be interesting for graduate students with knowledge in solid-state physics and quantum mechanics who are interested in optical spectroscopies of semiconductors.