Semiconductor nanostructures are currently one of the largest and most exciting areas in solid state physics. Low-dimensional electron systems (realized in semiconductor quantum structures) are particularly appealing because they allow one to study many-particle effects in reduced dimensions. Inelastic light scattering gives direct access to the elementary excitations of those systems. After an overview of the basic concepts and fabrication techniques for nanostructures on an introductory level, and an introduction into the method of inelastic light scattering, this monograph presents a collection of recent advances in the investigation of electronic elementary excitations in semiconductor nanostructures