Photon (x-ray, gamma-ray, bremsstrahlung) mass attenuation coefficients, mu/rho, are among the most widely used physical parameters employed in medical diagnostic and therapy computations, as well as in diverse applications in other fields such as nuclear power plant shielding, health physics and industrial irradiation and monitoring, and in x-ray crystallography. This review traces the evolution of this data base from its empirical beginnings totally derived from measurements beginning in 1907 by Barkla and Sadler and continuing up through the 1935 Allen compilation (published virtually unchanged in all editions up through 1971-1972 of the Chemical Rubber Handbook), to the 1949 semi-empirical compilation of Victoreen, as our theoretical understanding of the constituent Compton scattering, photoabsorption and pair production interactions of photons with atoms became more quantitative. The 1950s saw the advent of completely theoretical (guided by available measured data) systematic compilations such as in the works of Davisson and Evans, and by White-Grodstein under the direction of Fano, using mostly theory developed in the 1930s (pre-World War II) by Sauter, Bethe, Heitler and others. Post-World War II new theoretical activity, and the introduction of the electronic automatic computer, led to the more extensive and more accurate compilations in the 1960s and 1970s by Storm and Israel, and by Berger and Hubbell. Today's mu/rho compilations by Cullen et al, by Seltzer, Berger and Hubbell, and by others, collectively spanning the ten decades of photon energy from 10 eV to 100 GeV, for all elements Z= 1 to 100, draw heavily on the 1970s shell-by-shell photoabsorption computations of Scofield, the 1960s coherent and incoherent scattering computations of Cromer et al, and the 1980 computations of electron-positron pair and triplet computations of Hubbell, Gimm and Øverbø, these names being representative of the vast legions of other researchers whose work fed into these computations.