A New Monte Carlo code (EBUF) is developed to calculate improved point isotropic photon exposure buildup factors in media. Variance reduction techniques are used to perform calculations up to 60 mean free paths. EBUF accounts for coherent scattering and bound-electron Compton scattering. Bremsstrahlung photons and annihilation gamma rays as well as K and L X-rays are considered. The most recent cross-section data are used. The EBUF exposure buildup factors compare very well with those from the ANS-6.4.3 Working Group (ANS-6.4.3) when the same initial conditions are assumed: no coherent scattering, free-electron Compton scattering, and only K X-ray fluorescence. Next, a detailed physics treatment is used to calculate a representative set of exposure buildup factors in aluminum, iron, lead, water, air, and concrete over a large energy range (20 keV to 10 MeV). The effects of L X-rays are shown for lead at low energy. The EBUF factors are in good agreement with the SN1D code results for low-Z media. Finally, total exposure values from EBUF and ANS-6.4.3 are compared. Quite significant differences are observed because the ANS-6.4.3 calculations do not account for binding effects in Compton scattering, L X-ray fluorescence, and coherent scattering in mixtures.