Book excerpt: Compton Scattering has become a standard tool to study the electron momentum densities in materials because the momentum distribution of valence electrons in a solid can be measured through the Doppler shift of Compton scattered photons by electrons in motion. This book details how the Compton scattering experiments are performed, data are analyzed, and results are interpreted and provides fundamental understanding of the electronic structure and momentum density of some Ti-based alloys and semiconductors compounds.