In the last ten years, the physics and technology of low dimensional structures has experienced a tremendous development. Quantum structures with vertical and lateral confinements are now routinely fabricated with feature sizes below 100 run. While quantization of the electron states in mesoscopic systems has been the subject of intense investigation, the effect of confinement on lattice vibrations and its influence on the electron-phonon interaction and energy dissipation in nanostructures received atten tion only recently. This NATO Advanced Research Workshop on Phonons in Sem iconductor Nanostructures was a forum for discussion on the latest developments in the physics of phonons and their impact on the electronic properties of low-dimensional structures. Our goal was to bring together specialists in lattice dynamics and nanos tructure physics to assess the increasing importance of phonon effects on the physical properties of one-(lD) and zero-dimensional (OD) structures. The Workshop addressed various issues related to phonon physics in III-V, II-VI and IV semiconductor nanostructures. The following topics were successively covered: Models for confined phonons in semiconductor nanostructures, latest experimental observations of confined phonons and electron-phonon interaction in two-dimensional systems, elementary excitations in nanostructures, phonons and optical processes in reduced dimensionality systems, phonon limited transport phenomena, hot electron effects in quasi - ID structures, carrier relaxation and phonon bottleneck in quantum dots.