The diffraction of X-rays is used as the main method for determining the atomic and molecular structures of inorganic and biological materials. The basic law of diffraction was discovered by Lawrence Bragg when he was a student at Cambridge University and he was just 22 years old. Bragg’s law explains how the angle of a diffracted X-ray beam varies with the wavelength of the X-rays and the spacing of the atoms and molecules in the material. This chapter examines the way X-rays are generated and scattered by electrons, atoms and crystals; the use of structure factors and Fourier transforms to calculate the intensity of the scattered X-rays; and the effect of using electrons or neutrons instead of X-rays. Bragg was born and brought up in Adelaide in Australia. He discovered Bragg’s law with the help of his father, William, after they had moved to England. Lawrence was a Professor at Manchester University, Cambridge University, and the Royal Institution; contributed to the development of range-finding, asdic, and sonar during the First and Second World Wars; and supervised Crick and Watson when they discovered the structure of DNA.